Solution
= Solution
For $f=x^2$, $\int_{-1}^1x^4dx=2/5$, $a_0=2/3$, and $a_n=4(-1)^n/(\pi^2n^2)$. Parseval yields $2/5=2/9+16\pi^{-4}\sum n^{-4}$, hence $\sum n^{-4}=\pi^4/90$.
= Solution
For $f=x^2$, $\int_{-1}^1x^4dx=2/5$, $a_0=2/3$, and $a_n=4(-1)^n/(\pi^2n^2)$. Parseval yields $2/5=2/9+16\pi^{-4}\sum n^{-4}$, hence $\sum n^{-4}=\pi^4/90$.