Im struggling with a Fourier series and would like some help.
$f(x) = x-x^2$ has the Fourier series $\frac{1}{6} - \sum_{n=1}^{\infty} \frac{1}{n^2 \pi^2} \cos(2n \pi x)$ and i want to calculate $\sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n^2}$
Why do we want to set $x=\frac{1}{2}$ to solve it? How do I know what to set $x$ to?
Thanks!