Calculate the series: $\sum^\infty_{n=1}\frac{(-1)^n}{n^2}$ using dirichlet's theorem This question was in my exam:
Calculate the series: $$\sum^\infty_{n=1}\frac{(-1)^n}{n^2}$$.
I answered wrong and the teacher noted:  "You should use dirichlet's theorem".
I know my question is a bit general,
but can you please explain me how should I have solved this sum?
Thanks in advance.

Jack's answer is perfectly all right.
If you want to use Dirichlet's theorem from the theory of Fourier series, consider the $2\pi$-periodic function $f$ such that $f(x)=x^2$ on $[-\pi,\pi)$.
