Sum of series VII
What is the sum of the following sequence:
Σ(km^k)/(k+m)! for k=1...n
for different n and m?
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Sum of series VI
What is the sum of the following sequence:
Σk⋅k! for k=1...n
for different n?
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Sum of series V
What is the sum of the following sequence:
Σk(k+1) for k=1...n
for different n?
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Sum of series IV
What is the sum of the following sequence:
Σ(-1)^(k+1) (2k-1)^2 for k=1...n
for different n?
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Sum of series III
What is the sum of the following sequence:
Σ(2k-1)^3 for k=1...n
for different n?
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Sum of series II
What is the sum of the following sequence:
Σ(2k-1)^2 for k=1...n
for different n?
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Sum of series I
What is the sum of the following sequence:
Σ(2k-1) for k=1...n
for different n?
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Dimensions of a rectangle
The longer side of a rectangle is three times the length of the shorter side. If the length of the diagonal is x, find the width...
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Is this triangle right-angled?
Given three positive numbers a, b, c, where c is the largest number, return true if the triangle with sides a, b and c is right-...
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Is this triangle right-angled?
Given any three positive numbers a, b, c, return true if the triangle with sides a, b and c is right-angled. Otherwise, return f...
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Find a Pythagorean triple
Given four different positive numbers, a, b, c and d, provided in increasing order: a < b < c < d, find if any three of them com...
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Triangle sequence
A sequence of triangles is constructed in the following way:
1) the first triangle is Pythagoras' 3-4-5 triangle
2) the second...
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Length of a short side
Calculate the length of the short side, a, of a right-angled triangle with hypotenuse of length c, and other short side of lengt...
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Triangle Coordinates
Given a natural number n, return two -element vectors, x and y, containing the coordinates of a triangular arrangement of points...
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Extract the Acrostic Message
An acrostic cipher is a way of embedding one message within another by taking the first (or last) word of each line. Given a str...