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,