how to calculate alternating summation for pi

How do I write code to estimate pi up to 1 million terms (n=1million) of: pi = 4(1/1 - 1/3 + 1/5 - 1/7 +...etc)

Answer 1

[Star Strider]

Use MATLAB vectors:

N = 1E+6;                                               % Number Of Terms
N = 2*fix(N/2);                                         % Assure Even Number Of Terms
sgn = -(-1).^[1:N];                                     % Sign Vector
denom = 1:2:2*N;                                        % Denominator Vector
pie = 4*sum(1./(denom.*sgn))                            % Desired Result
error = pi - pie                                        % Difference Between Our Calculation And MATLAB ‘pi’

pie =
          3.14159165358978

error =
      1.00000001213019e-06

[John Jamison]

for the 'sgn' and 'denom' steps, how could you make those into vector equations—i.e 'v =' ?

[Star Strider]

I’m not certain what you mean by ‘vector equations—i.e 'v =' ’ A more detailed description or explanation would be helpful.

They are already ‘vector equations’ as I interpret it. I combined them in the ‘pie’ assignment. You can break them out as a single vector and then calculate ‘pie’ as:

v = denom.*sgn;
pie = 4*sum(1./v)

While I’m thinking about it, remember to celebrate International Pi Day (to three significant digits) on March 14 (3 14 2017).

Answer 2

[KSSV]

You may refer this link:

https://in.mathworks.com/matlabcentral/answers/56535-estimating-the-value-of-pi-using-a-summation-through-creation-of-an-m-file-by-using-a-loop

[John Jamison]

I don't understand loops. How can I solve it simpler without the 'while' and 'end'?