$\begingroup$

I have a question about

$\sum_{n=1}^{\infty} 1/n^2$ = $\pi^2/6$

I know it can be proven with standard 1 variable analysis (working on Taylor series of $\arcsin$ or something like that) or basic complex analysis. But someone told me it has also great prove using Functional Analysis. He suggested it is proved on standard first course of FA, but it was not in my case. Can You write here the proof using FA or leave a link in comment? Thanks in advance.

Answers