I'm trying to find the sum of the infinite series:
using the Fourier series of x^2 on [-pi, pi] which I have as
PI^2/3 + 4*sum(n=1..infinity) (-1)^n/n^2*cos(nx)
The Attempt at a Solution
So far all my attempts have been focused on finding a the series at various points in [-pi, pi] and seeing if I can add all the series together to cancel out the terms I don't need or leave the series I want with another series that I know the sum for. However, so far all these attempts have been unsuccessful and I think that since most of these equations seem fairly unwieldy that I'm just missing a small detail that would make this problem easily solvable. Anyone have any suggestion as to where to start on this problem so I can see if I can take it from there?