Evaluate Series: sin(pi)(sq. rt. (n^2+k^2))

A00446849 · 2007-07-01T19:07:37+00:00

Homework Statement sigma n=1 to infinity sin(pi)(sq. rt. (n^2 + k^2)) Homework Equations The Attempt at a Solution

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply

. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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Homework Statement

Homework Equations

The Attempt at a Solution

Thread 'Finding the nth roots of a complex number'

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