Basel Problem/Proof 7

Proof
By Fourier Series of $x^2$, for $x \in \openint {-\pi} \pi$:


 * $\displaystyle x^2 = \frac {\pi^2} 3 + \sum_{n \mathop = 1}^\infty \paren {\paren {-1}^n \frac 4 {n^2} \cos n x}$

Letting $x \to \pi$ from the left: