Sure, a Fourier series would be straightforward.
I'm familiar w/ how Fourier analysis can be used to sum the first series, but it's not immediately clear to me how to proceed from that solution, to the sum for the second series.
Could you give me a pointer/hint?
The Basel Problem is a well known result in analysis which basically states:
\frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + ... = \frac{\pi^2}{6}
There are various well-known ways to prove this.
I was wondering if there is a similar, simple way to calculate the value of the...