I have this function: $f(t) = \frac{1}{12} (\pi^2 t-t^3)$ and I have a Fourier series defined by:
$$f(t) = \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n^3} \sin (nt)$$
I am then suppose to show that this is true:
$$\sum_{n=1}^{\infty}\frac{1}{n^6} = \frac{\pi^6}{945}$$
I tried doing something like this a few times where you just have to input a $t$ where the function is continuous (like $t = \frac{\pi}{2}$ or something like that), but I just cant seem to figure out a $t$ that makes this true.. Are there other ways of doing it?