find a half-range series of $\displaystyle f(x)=x^{2} \ \ in \ \ (0,1) $

and then show that:

$\displaystyle \sum_{n=1}^{\infty}{\frac{1}{n^{2}}}=\frac{\pi^{2} }{6} $

i got a series:

$\displaystyle x^{2}=\frac{4}{3}+\sum_{n=1}^{\infty}{\frac{4(-1)^{n}}{n^{2}\pi^{2}}\cos(n\pi x) } $