Alternating series

$\begin{align} &S_1=\displaystyle\sum\limits_{n=1}^{\infty }{\frac{{{\left( -1 \right)}^{n}}}{n^2}} \\\\ &S_2=\displaystyle\sum\limits_{n=1}^{\infty }{\frac{1}{n^2}} \end{align}$ **Which series converges?** [[☃ radio 1]] **Based on your answer, what can we say about $S_1$?** [[☃ radio 2]]