How can I use Parseval's theorem to find the summation from n =1 to infinity of (1/n^4)?
I'm pretty sure I can calculate the Fourier cosine or sine series for a function; however, I'm not sure what this function should be. I tried f(x) = x, but I get something with (-1)^n - 1 in the numerator with n^2 in the denominator. Because it has this oscillating part, I can't solve the summation.
Tough to explain I guess, but does anyone have an idea what function to use and how you do it? I've been trying to get 1/n^2 in the denominator of the an terms (and then you square it), but I can't get it with just constants. I know the answer is pi/90. I would appreciate any help.