Basel Problem/Proof 8

Proof
By Fourier Series of $x$, for $x \in \left({- \pi \,.\,.\, \pi}\right)$:


 * $\displaystyle x = 2 \sum_{n \mathop = 1}^\infty \frac {\left({-1}\right)^{n + 1} } n \sin \left({n x}\right)$

Hence: