{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":60456,"title":"Compute a sum","description":"Write a function to compute the following sum\r\n\r\nAlthough a solution is available for general values of the coefficients, the coefficients are chosen so that a simpler form is possible. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 126px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 63px; transform-origin: 407px 63px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 141.067px 8px; transform-origin: 141.067px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the following sum\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"123.5\" height=\"45\" alt=\"S = Sum[(an+b) u^n/(n*(n+m)*v^n),{n,1,Infinity}]\" style=\"width: 123.5px; height: 45px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375.108px 8px; transform-origin: 375.108px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAlthough a solution is available for general values of the coefficients, the coefficients are chosen so that a simpler form is possible. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = JPMsum1(a,b,m,u,v)\r\n  y = sum([v u m b a]);\r\nend","test_suite":"%%\r\na = 4;\r\nb = 9;\r\nm = 1; \r\nu = 5;\r\nv = 9;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 5;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 7;\r\nb = 32;\r\nm = 2; \r\nu = 3;\r\nv = 4;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 16.5;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 168;\r\nb = 1058;\r\nm = 2; \r\nu = 19;\r\nv = 23;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 617.5;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 19;\r\nb = 81;\r\nm = 3; \r\nu = 2;\r\nv = 3;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 80/3;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 547;\r\nb = 8232;\r\nm = 3; \r\nu = 13;\r\nv = 14;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 13390/3;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 6095;\r\nb = 82944;\r\nm = 4; \r\nu = 11;\r\nv = 12;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 36704.25;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 469711;\r\nb = 9447840;\r\nm = 5; \r\nu = 17;\r\nv = 18;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 3817735.9;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 117585;\r\nb = 705894;\r\nm = 6; \r\nu = 2;\r\nv = 7;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 593732/15;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\nfiletext = fileread('JPMsum1.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'switch') || contains(filetext, 'if'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":6,"created_by":46909,"edited_by":46909,"edited_at":"2024-06-09T16:09:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":"2024-06-09T16:09:49.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-06-09T02:41:38.000Z","updated_at":"2026-02-01T07:00:29.000Z","published_at":"2024-06-09T02:41:38.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the following sum\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S = Sum[(an+b) u^n/(n*(n+m)*v^n),{n,1,Infinity}]\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS = \\\\sum_{n = 1}^\\\\infty \\\\frac{an+b}{n(n+m)} \\\\frac{u^n}{v^n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAlthough a solution is available for general values of the coefficients, the coefficients are chosen so that a simpler form is possible. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60633,"title":"Sum the reciprocals of polygonal numbers","description":"As explained in Cody Problem 60571, a polygonal number is the number of dots arranged in the shape of a regular polygon. For example, 15 is a triangular number because dots can be arranged in the shape of a triangle with rows of 1, 2, 3, 4, and 5 dots. The number 16 is a square number because dots can be arranged in four rows of four. \r\nWrite a function to sum the reciprocals of polygonal numbers. In particular, compute\r\n\r\nwhere  is the th -gonal number (i.e., the th number corresponding to a regular polygon with  sides).  ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 178px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 89px; transform-origin: 407px 89px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.4083px 8px; transform-origin: 49.4083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs explained in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/60571\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 60571\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Polygonal_number\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003epolygonal number\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 203.483px 8px; transform-origin: 203.483px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of dots arranged in the shape of a regular polygon. For example, 15 is a triangular number because dots can be arranged in the shape of a triangle with rows of 1, 2, 3, 4, and 5 dots. The number 16 is a square number because dots can be arranged in four rows of four. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 258.533px 8px; transform-origin: 258.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to sum the reciprocals of polygonal numbers. In particular, compute\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"74\" height=\"45\" alt=\"y = sum[1/P_n,s,{n,1,inf}]\" style=\"width: 74px; height: 45px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"23.5\" height=\"20\" alt=\"P_n,s\" style=\"width: 23.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6083px 8px; transform-origin: 20.6083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 8px; transform-origin: 7.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003es\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 74.2917px 8px; transform-origin: 74.2917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-gonal number (i.e., the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.942px 8px; transform-origin: 157.942px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth number corresponding to a regular polygon with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003es\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.5px 8px; transform-origin: 24.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e sides). \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = sumRecipPolyNum(s)\r\n   y = sum(1/s);\r\n","test_suite":"%%\r\nn = 3;\r\ny = sumRecipPolyNum(n);\r\ny_correct = 2;\r\nassert(abs(y-y_correct)\u003c1e-13)\r\n\r\n%%\r\nn = 4;\r\ny = sumRecipPolyNum(n);\r\ny_correct = 1.644934066848226;\r\nassert(abs(y-y_correct)\u003c1e-13)\r\n\r\n%%\r\nn = 7;\r\ny = sumRecipPolyNum(n);\r\ny_correct = 1.32277925312239;\r\nassert(abs(y-y_correct)\u003c1e-13)\r\n\r\n%%\r\nn = 11;\r\ny = sumRecipPolyNum(n);\r\ny_correct = 1.19543411652963;\r\nassert(abs(y-y_correct)\u003c1e-13)\r\n\r\n%%\r\nn = 18;\r\ny = sumRecipPolyNum(n);\r\ny_correct = 1.11589671405633;\r\nassert(abs(y-y_correct)\u003c1e-13)\r\n\r\n%%\r\nn = 24:26;\r\ny = arrayfun(@sumRecipPolyNum,n);\r\ns = sum(y);\r\ns_correct = 3.247536806913290;\r\nfor k = 1:3\r\n    str = num2str(y(k),'%1.15f');\r\n    z(k) = str2num(flip(str(11:14)));\r\nend\r\nfs = sum(factor(sum(z)));\r\nfs_correct = 185;\r\nassert(abs(s-s_correct)\u003c1e-13)\r\nassert(isequal(fs,fs_correct))\r\n\r\n%%\r\nn = 31;\r\nindx = [4 5 7 9 10 11];\r\ns = num2str(sumRecipPolyNum(n),'%1.15f');\r\nd = num2str(sumRecipPolyNum(str2num(s(indx(randi(6))))),'%1.15f')-'0';\r\np = prod(d(3:13));\r\np_correct = 186624;\r\nassert(isequal(p,p_correct))\r\n\r\n%%\r\nn = 57;\r\ns = num2str(sumRecipPolyNum(n),'%1.15f');\r\nindx = [3 4; 4 10; 6 7; 7 10; 8 9; 8 10];\r\nfor k = size(indx,1):-1:1\r\n    a(k) = str2num(s(indx(k,1):indx(k,2)));\r\nend\r\nassert(all(isprime(a)))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-07-16T01:35:12.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-07-16T01:34:17.000Z","updated_at":"2025-10-01T15:44:42.000Z","published_at":"2024-07-16T01:35:12.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs explained in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/60571\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 60571\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Polygonal_number\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epolygonal number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of dots arranged in the shape of a regular polygon. For example, 15 is a triangular number because dots can be arranged in the shape of a triangle with rows of 1, 2, 3, 4, and 5 dots. The number 16 is a square number because dots can be arranged in four rows of four. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to sum the reciprocals of polygonal numbers. In particular, compute\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y = sum[1/P_n,s,{n,1,inf}]\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = \\\\sum_{n=1}^\\\\infty \\\\frac{1}{P_{n,s}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"P_n,s\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP_{n,s}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"s\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e-gonal number (i.e., the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth number corresponding to a regular polygon with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"s\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e sides). \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":60456,"title":"Compute a sum","description":"Write a function to compute the following sum\r\n\r\nAlthough a solution is available for general values of the coefficients, the coefficients are chosen so that a simpler form is possible. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 126px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 63px; transform-origin: 407px 63px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 141.067px 8px; transform-origin: 141.067px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the following sum\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPcAAABaCAYAAABkDsBjAAASJklEQVR4Xu2dV8g2RxXHv4AXImiwXNn4UHMRElCCDaOCQqwgir1cvKDEiiD2GAmCLRaCYidCCIoliiJELBAhEdFYUBQULEgQr6zkwhtBz0/3/+V88872md1nnz0Lh7fs7O7MmfOfOW1mLjgTV3AgOHCUHLjgKFsVjQoOBAfOBLhDCIIDR8qBAPeRdmw0KzgQ4A4ZCA4cKQcC3EfasdGs4ECAO2QgOHCkHAhwH2nHRrOCAwHukIHgwJFyIMA9rGMfbsWe2hT9iv38Q/LYfe3vi43+nLk37AtRKjhQmAMB7n6GftGKPNLo7+7n2+33TzePvsV+Xute8237/TUB8n7GRom6HAhwd/MX4F5p9Bijvxq9yOgLzSNPsJ8PbP7+kv38mdGTjZjhf2L0tOaZuj0Ybw8OtHAgwN0tGn9rZmFmb12aqX9v/7iPkZ/FKUPZFxo90+ibIXnBgbU4EOBu5zx29s9bQPqtZoZmxmY295eee6/98x1rdWx8NzgQ4G6XgcfbrduMXmUk+1qldU92eOpg+48VDHAHvlblQIC7nf0PsVuo3jn7+RP2/1c3j+JAw77Whef8L0bY5N9ftXfj47vmQIC7u/u9+n1jU/T19vPRRs8yusHooUZePccmf77Ro3YtWdH41TkQ4O7uAuzn7xnd2xVDFQfYzMrc/2oDcGZ57lFW3vXVOzgqsF8OBLj7+x41+wqjBxvdYfRdI8JiutL73rPe//YoERyoxIEAdyXGxmuDA2tzIMC9dg/E94MDlTgQ4K7E2HhtcGBtDgS41+6B+P6aHMAheqdRmqewZp2KfTvAXYyV8aINcIDko6uNcIKyGIjraNOE9wRu0kRPDkgA/2F1SVNXD6h6R12VHztw389+99GPQ244g9MlRkRu/mn0gUaGkOufGp2X7rwncL/SGv+ppOeIS99euDf9rND36shi6+NQnftKTiL7cEvJRoD7umZgQuO4vAE5KxdJpoLOmRh7Ajdi4kdsiU1NtUwjLbYds7RPhuH7uYUndcR5e28FgFyl18YrPZh3v9WI2W9L1++ssqxGJJ/i1uYncg2wMTV2C27yxRmt04yz85hSsaefYe8mfVW7uvCp80bbit/e2qtZfMP1CKNfFKw8fXBz876taU5a74DGCbgZ+DRYpWscdnniiO9cyczS6hkz+g0NsGP1WB65tcCtRT8A5CKjrdjbcEmmpa+75PmUFrI3tVxi5Fd16X9Lq2iMuB83esoGhazgRNr6qlrgRq1NF/ss0Z4S39BGIF5W32MvvsrolBayV3ADLGw6hUPE+DXUNOrBLL50Tjraw+saQWf2wnvPyjeZDeIFquD9jR5ndFlT/ib7KVtVW1EBmJLbS9UAt9Ra+lvr9PGFvNHJAuot4ClpCqTAxgdzz4anZ5tvpXsGeAewTDd2BuLyGofsbexw2rdbm9szuW3F19Kqmgaapby20hjYCgoBZzdXwK0dZOBRqvZdav97m5F8FdjBfzJiYNLAwPu4SmlANcCdAuZNVl80p88YATKt0acdtUJk8J9Vg+8y0uTyYvs9Hdzl/GW14cNc/3jbWoMVjllWL15odM5BuNeZu5HDczaM/ubnKceEv1npd4SO1Wa1M6W8xpLbYUaAynnxffgIIFPmeiNmHO1MA3ty753CthrgllqLhgFomAnfaSS72+9kW6odbW33pmE6kPiBVj4ZDUy+XipHW+iP3ca525isDvf3a3fsFGGf+4wHdpsTT4DqAj4z81kjZncJk98VtpT3vwa49U7tsPNaB2z46wep2o5Ozcw5Z67saOqkUK1U+XR3H/7PdcqMGDNz03DsLl0/sF/0IUaVH+Y+MFciF3geof+REULpr9IhmAWa0vkJDWIIdm4zCS/YKUD9vU/a86iDL3XAkDCOsbmlCczhCwMMtuaQy0dJ2va+8+0sZV7k6tYVa+feb41kAk02D4aAG6Z8tBF+VNZbmtqyRze2ABfCsGUw+E5VZ7SBYIggHVqZIWpzF0D9TJIDhjzQY2a7pcHt29CmmXm1vKZztSvW7uswK0TbB25fiRxDfMxw6Ah6aIKv+qQnh/B/ZikSBbZ+CUhtA5afLXJt9pl9qRx4D3RJQJRWyzUAdQ3aXlWueaiEBpo01p7O2rO0hz5we4ZolvaC3pods1E05GaTnCdzS83z4GsbrPzAlrbXP4/m5tVx+CB7u3RSSElw+za0aRdeu6nd5xpEUsclkyXee5mIswbLLnB7hnSpBwDi1IqULUm/q2tbeuqTrEzNuGdNdnlnV05o0zanNp5/Pqe9yZYvnSdfEty+DW3mowDHAOg96KX7xtvbnp9oyYTHqAchudmDZRe4/UjWpcoAbmzyYzk65xDSU0sKlJ+V00Uy8qATCvJnnHEG2gOaPhV424SNcBLOHwlqqbBeSXD3ORO9v4EwX82QpJcvDTQMsN9pZm1+MnMrJNvqDe8Tki5w+xGG97Tp/3ychIYt5ej28cU7X1R2jLOo7/1L3m+beQVsYtWvMCKhglmLuDXbNT/XCG1F4M3NzF5QEUj2c3+2URpimtLekuBWG3IaqPjDvdrAhg/+rDlMXfXDNfY7URsOtOBisCT3Ab5PqlefzZ3mYNdcHjlFAGo+s/Ty0FptSZ00DFJcqH46xNDHf7l3YqR92TkvjSun0nutgIGBLLtJgphpfClw+4QQD26fqcfE9VmjJSYo+XXQhHDWvtvog0ZpMhD9hP39hqYvRstHH7hTwaBCLzOaq4IzWrKbxNyr5lrctvTUpZaHzuWNf94v8tdyQYRJfgRvN3/MCZMHby45xdvrgPtDRqVU2lLghg+0/yVGyB0mJiBGtlGBv+z4UJLnbe/yWiF1YdsnpZ56Pxf9lJ4gO6p+feDmZamQ81GduDHqY67w0jHOqfX0Kq3esUZ66tT6b/k5bdZQexHHGjzqsqO1UOfXzSA0uX5DwF0D4CVmbvaQSlfSTGZEx4O59NRZ8ccalYx3BgdSDgwFdw7gSzkg1u61XHrqrMyhtRsU398HB8aAG46kYaKtepDH9m7bcsix74nywYHFODAW3FTMO1m01nSxCq/0ITkW+fyWE1pWYl98dg0O5MA9JClFcUPqPGXVSgmbm2/X9JarP/xSyT2FAteQx/hmQQ7kwE0+OVvtdIW7vLd7Cri34i2H1Yr1H+Ma74KiFK86NA7kwE18sc8b3LXQfEgbS8zcS3jLFZNce3WY15SG8DfKrMuBf9nn75FU4W72N3se1Lz+bS9/rD6Qgttv20J2TC4hIbfJXM0Kr/VuxbgPIa79EWPC3ddiRHx3NAcAGSm4/lod3N4bTk5rmiPs7c/Sq4BGc7DiA1o0M2ZnkYrViVcHB8ZzIJ25tU2tVqiwAQMqKSrwWSNmMy4SO45hE4Mcx5SRx70tppqOl4J44ig5kIKbmfs3RlLHUcFZ6aM88F/Z76xcWSLBfg2GK2GFQW0vIS8GsxcYnbdz5hrM38g3cbCWzKGv1uwpce5qlVn5xd7kqL0Tx8pNPfd5gH2tUbq7yqHU7xDrwYSHScoy2YPewCPAfZf4rBnyQmAwfZbUiAA267ZzO6EeIqgOqU7iXZvT+SDqGuD+fzco626tkBdx/yVnT5kfffkMByGkB1oJ/E8cQ7TUSTGj2RDgvmuDv7UWg7AtETPBkg5KtBS0BXb4jGs6BxiU2ep7iUzJ0bXcO7gV118r5KWQ25JprcpTmLWz5mhJ638AbeLiplh6qkb/0+uUUOi41Ckrfa3whzIyoMCz5zUP6cy3c+/YM7h9yGsNz7jOflp68Q2zNqrkoamTGujGnCLSB4Yl7pOufeqcrgofxgw4MWIjS773PiP2v+MiZHtqgtgruL1nfOmTUhBittahk7iWXDarTS/70osryGbvK7cKblKU2Y9uiUM5lA5N/3HiD2aV/EWnIjx7Bbdy45cKeemctSutM9IzyZZS6UCXUmoPTSWnblsFt1TzJXiaOxFFi7BOLeDaI7gV8kK1YTPAUpc/JJF3MrIyU+oM5tx3pjrxMCnYV5xLq/f41hVGJByRbJRb1ae2j+l3QMc+5uzppbguth/futCI3PsS8d6a4FYb2IJb9nxXG2TL0j5s2a5NH+XDqK0N+TUdflJioVdWjsZ0cikQrPme3Hlga9ZnjOaAjf4cI6nz1FvPM3t8zkgnQ3Iv56RjlCfjsE+FlF3uByZpGCkP207MHMvX0uBGS2EPdbZa1iUTjHu0Ufzyh26kvBzibAVgtddaSOvyPhrxLGva7QncuZNExgpg6fJT1sJLNdMJIMyg7H19YnQvo5ubSuY6HCEcusrNH0qhZxRCI2z3cqOrmm+V8PaXBrf6yvOLQQ2QwC8SUHwb6Avxkvj/5a59ff3EktzbjcaEFmkv/fUgo9xGnwzmaA4Ks0nr8hOCBtqsSbAncCuMUBqgU993pz04RZ3V4YwyK26w9yjLzB8BlevwMeBOl/YiaJc14KDNEqzZZ1o1DKwFbu1/ToLSrQ2wxS8BhtmZzf89L3VvSDRjqEZEU5lkLjXy/pd08PD9qMQq9bsvq4GL/1GH8yIgewL3VBAe0nMp4N5slTsxkh3ZB7gx4PZ7tjNbMNv5VFU5coZqAhoQ2vh51m7oALz3dzD9DrunTfz7+sZvbIkmg4ru2+AP/2Mm1xFKvFdgGpK1KF6MwZPXJHOajwYX+IumxCCT8pr+5P8MsKeOHB5TmT5Gxv1uDkgNm3NaiwccnapjaPTlvhM3x4BbwoXgoHb6QYTvpQcADul/zaJDyraVGWPbKpeANsAvfzSPNzu6Tv4YYnJMATftEz/anHHaFQlQ42tJnZfSArJHIQW454jZsGeZbTVrzI1p+wMScjOmhKVtv7cx4PZbO6XC59XGMXkCaBZt11m7wczNxffarrZIQK6851fKez9zprz0g2ifvc13meWhMTY3z2lQyA1YSrKavKdAgHsYQKeWAgSXGJEBh0o4F9wCHDNRmlXnAdcWO0cN5erLTvPqbM7mlPo/xB4dyrsaNrcGu1zWmzQT6pcOUN4W7+MVz48ZND0/NPjkQlnUgXpPXmcf4B4qevPKCQxzwJ1zsvhaKXupC3ASpr5+9+GuXLjO26qlFryUBrefmXNqr3dMaoch8VP3hsSu52T9tflI4MU3jC4ymrwMuK+T54l0PC0OlAC3Px0ypwoLcBpAMAfS5AvZoH2qdBo+8j3pbVXZo7lvje390uD2M3OqybQlhFBnf08Rh672qd5DbPOUJ34Qlfqv5bgnVnjWApq9g1srkVCdOegcMGjb5b7MpDHCWwLcAlxuZk4FkmyyzxulJ2SqXFfyjAdvzlMse1QhMLLXrjcaor528aw0uDX75nwT3tGWzo5p+4h9kwyTzu5qiwbdIbZ52n6vXeh5BqU/Gs1eRrpncCNMnNms8AudDCC48ExqBqRcmlraJaQ5h89ccHvA5VRFCSv1YpbCQfNho1zIiEGCAaJNWL3A5WLl3k5kqyF2c/EhpC7eLAVu7zPIORe7wngCq2Lf11mlT4WZXEPgJzTFPEnzEp7e9F9b34zi7Z7BDaMkyMxQzDx0ImuKbzPSrKWldkMZ+zUrmGYczQW3997mAOfvU8+u01FUts3p5kNgOZvPq7vM3nPPahdfS87c6WDnzZO+gVLAp14+LTXX/xpEpi4a8eBmQOYqAmxetHdw+1H6GuMHMWgBcYoN1TYAzAW31x7a1DWlKw4xJ5hpbjLKvUtmSVuyCOAgbZM9305tEDB0BMyUKwnurjZgmvgNDlK/BIBFcxuSLMNAp5TWKU334C4ZefhfXfYO7lwWUusSuim91zwzF9wzPp19VDPOkstN+9qwtZ1Y5NGeHIc2hgjc+AWK76G3Z3B7J5QX8nQJ3SHY3H3AmHKf2e2gN/ib0qiFnim5wST9MDSddlTz9gxu2Z7eI6yR1DutDsHmHtWpIwqjUZw1muIMGvGZoysKGL9eC5SluLVncMsx5G1r2eA4SK5uhL5rof7Qfjg0tdzXm8HriQHwoV15Bhn55aEDm9bsGdyytz0PfK7vjcafOYs8vLR05RAPlqqKBVEzJ2dCVazXIb66RMLOIu3aK7jl8U1j0vKUlto6yG/low7FC8vC/hIawSJCEh/ZJgf2Cu5t9lbUOjgwggMB7hHMiqLBgS1xIMC9pd6KugYHRnAgwD2CWVE0OLAlDgS4t9RbUdfgwAgOBLhHMCuKBge2xIEA95Z6K+oaHBjBgf8C4nmml5JfGEAAAAAASUVORK5CYII=\" width=\"123.5\" height=\"45\" alt=\"S = Sum[(an+b) u^n/(n*(n+m)*v^n),{n,1,Infinity}]\" style=\"width: 123.5px; height: 45px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375.108px 8px; transform-origin: 375.108px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAlthough a solution is available for general values of the coefficients, the coefficients are chosen so that a simpler form is possible. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = JPMsum1(a,b,m,u,v)\r\n  y = sum([v u m b a]);\r\nend","test_suite":"%%\r\na = 4;\r\nb = 9;\r\nm = 1; \r\nu = 5;\r\nv = 9;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 5;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 7;\r\nb = 32;\r\nm = 2; \r\nu = 3;\r\nv = 4;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 16.5;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 168;\r\nb = 1058;\r\nm = 2; \r\nu = 19;\r\nv = 23;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 617.5;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 19;\r\nb = 81;\r\nm = 3; \r\nu = 2;\r\nv = 3;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 80/3;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 547;\r\nb = 8232;\r\nm = 3; \r\nu = 13;\r\nv = 14;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 13390/3;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 6095;\r\nb = 82944;\r\nm = 4; \r\nu = 11;\r\nv = 12;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 36704.25;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 469711;\r\nb = 9447840;\r\nm = 5; \r\nu = 17;\r\nv = 18;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 3817735.9;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 117585;\r\nb = 705894;\r\nm = 6; \r\nu = 2;\r\nv = 7;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 593732/15;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\nfiletext = fileread('JPMsum1.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'switch') || contains(filetext, 'if'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":6,"created_by":46909,"edited_by":46909,"edited_at":"2024-06-09T16:09:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":"2024-06-09T16:09:49.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-06-09T02:41:38.000Z","updated_at":"2026-02-01T07:00:29.000Z","published_at":"2024-06-09T02:41:38.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the following sum\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S = Sum[(an+b) u^n/(n*(n+m)*v^n),{n,1,Infinity}]\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS = \\\\sum_{n = 1}^\\\\infty \\\\frac{an+b}{n(n+m)} \\\\frac{u^n}{v^n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAlthough a solution is available for general values of the coefficients, the coefficients are chosen so that a simpler form is possible. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60633,"title":"Sum the reciprocals of polygonal numbers","description":"As explained in Cody Problem 60571, a polygonal number is the number of dots arranged in the shape of a regular polygon. For example, 15 is a triangular number because dots can be arranged in the shape of a triangle with rows of 1, 2, 3, 4, and 5 dots. The number 16 is a square number because dots can be arranged in four rows of four. \r\nWrite a function to sum the reciprocals of polygonal numbers. In particular, compute\r\n\r\nwhere  is the th -gonal number (i.e., the th number corresponding to a regular polygon with  sides).  ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 178px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 89px; transform-origin: 407px 89px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.4083px 8px; transform-origin: 49.4083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs explained in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/60571\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 60571\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Polygonal_number\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003epolygonal number\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 203.483px 8px; transform-origin: 203.483px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of dots arranged in the shape of a regular polygon. For example, 15 is a triangular number because dots can be arranged in the shape of a triangle with rows of 1, 2, 3, 4, and 5 dots. The number 16 is a square number because dots can be arranged in four rows of four. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 258.533px 8px; transform-origin: 258.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to sum the reciprocals of polygonal numbers. In particular, compute\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"74\" height=\"45\" alt=\"y = sum[1/P_n,s,{n,1,inf}]\" style=\"width: 74px; height: 45px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"23.5\" height=\"20\" alt=\"P_n,s\" style=\"width: 23.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6083px 8px; transform-origin: 20.6083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 8px; transform-origin: 7.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003es\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 74.2917px 8px; transform-origin: 74.2917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-gonal number (i.e., the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.942px 8px; transform-origin: 157.942px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth number corresponding to a regular polygon with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003es\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.5px 8px; transform-origin: 24.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e sides). \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = sumRecipPolyNum(s)\r\n   y = sum(1/s);\r\n","test_suite":"%%\r\nn = 3;\r\ny = sumRecipPolyNum(n);\r\ny_correct = 2;\r\nassert(abs(y-y_correct)\u003c1e-13)\r\n\r\n%%\r\nn = 4;\r\ny = sumRecipPolyNum(n);\r\ny_correct = 1.644934066848226;\r\nassert(abs(y-y_correct)\u003c1e-13)\r\n\r\n%%\r\nn = 7;\r\ny = sumRecipPolyNum(n);\r\ny_correct = 1.32277925312239;\r\nassert(abs(y-y_correct)\u003c1e-13)\r\n\r\n%%\r\nn = 11;\r\ny = sumRecipPolyNum(n);\r\ny_correct = 1.19543411652963;\r\nassert(abs(y-y_correct)\u003c1e-13)\r\n\r\n%%\r\nn = 18;\r\ny = sumRecipPolyNum(n);\r\ny_correct = 1.11589671405633;\r\nassert(abs(y-y_correct)\u003c1e-13)\r\n\r\n%%\r\nn = 24:26;\r\ny = arrayfun(@sumRecipPolyNum,n);\r\ns = sum(y);\r\ns_correct = 3.247536806913290;\r\nfor k = 1:3\r\n    str = num2str(y(k),'%1.15f');\r\n    z(k) = str2num(flip(str(11:14)));\r\nend\r\nfs = sum(factor(sum(z)));\r\nfs_correct = 185;\r\nassert(abs(s-s_correct)\u003c1e-13)\r\nassert(isequal(fs,fs_correct))\r\n\r\n%%\r\nn = 31;\r\nindx = [4 5 7 9 10 11];\r\ns = num2str(sumRecipPolyNum(n),'%1.15f');\r\nd = num2str(sumRecipPolyNum(str2num(s(indx(randi(6))))),'%1.15f')-'0';\r\np = prod(d(3:13));\r\np_correct = 186624;\r\nassert(isequal(p,p_correct))\r\n\r\n%%\r\nn = 57;\r\ns = num2str(sumRecipPolyNum(n),'%1.15f');\r\nindx = [3 4; 4 10; 6 7; 7 10; 8 9; 8 10];\r\nfor k = size(indx,1):-1:1\r\n    a(k) = str2num(s(indx(k,1):indx(k,2)));\r\nend\r\nassert(all(isprime(a)))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-07-16T01:35:12.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-07-16T01:34:17.000Z","updated_at":"2025-10-01T15:44:42.000Z","published_at":"2024-07-16T01:35:12.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs explained in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/60571\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 60571\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Polygonal_number\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epolygonal number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of dots arranged in the shape of a regular polygon. For example, 15 is a triangular number because dots can be arranged in the shape of a triangle with rows of 1, 2, 3, 4, and 5 dots. The number 16 is a square number because dots can be arranged in four rows of four. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to sum the reciprocals of polygonal numbers. In particular, compute\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y = sum[1/P_n,s,{n,1,inf}]\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = \\\\sum_{n=1}^\\\\infty \\\\frac{1}{P_{n,s}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"P_n,s\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP_{n,s}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"s\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e-gonal number (i.e., the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth number corresponding to a regular polygon with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"s\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e sides). \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"term":"tag:\"partial 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