"For $f(x) = x^2$ on the interval $[-1,1]$ with period $2$, determine the Fourier series.
Show that $\pi^2 / 6 = \sum_{n=1}^{\infty}(1/n^2)$".
How is the first part of this exercise related to the last?
EDIT: Found the solution. Simply do the initial part of the problem and then the latter part of the exercise follows easily.
The relevant Fourier series is $$ x^2= {1\over 3}+\sum_{n=1}^\infty {4(-1)^n\over n^2\pi^2}\cos(n\pi x), \quad -1<x<1. $$ Evaluating at $x=1$ $$ 1^2={1\over 3}+\sum_{n=1}^\infty {4\over n^2\pi^2}, $$ and a little rearranging: $$ {\pi^2\over 6}=\sum_{n=1}^\infty {1\over n^2}. $$