How can you solve for the summation term, $\sum_{n=1}^{\infty} \frac{(-1)^n}{(n\pi)^2}$, in the Fourier series below?
$$ x^2 \thicksim \frac{1}{3} + 4\sum_{n=1}^{\infty} \frac{(-1)^n}{(n\pi)^2}\cos{n\pi x} $$
After rearranging the terms, I'm stuck at dividing out the cosine term from the summation.
$$ \frac{x^2}{4} - \frac{1}{12} \thicksim \sum_{n=1}^{\infty} \frac{(-1)^n}{(n\pi)^2}\cos{n\pi x} $$