I know that the infinite sum of the reciprocals of squares converges to $\pi^2/6$. Interested by this, I looked at a different sum. It is similar to the previously mentioned series, but it alternates signs: $\sum_{i=1}^n \frac{(-1)^{i+1}}{i^2}$. I tried adding up the first several terms but I could not identify any interesting convergence (up to $\ n=14$ the sum is 0.82009731292). Is it possible that the series does not converge?
Thanks.