Is the series $\sum _{n=1}^{\infty } (-1)^n / {n^2}$ convergent or absolutely convergent? Is this series convergent or absolutely convergent? $$\sum _{n=1}^{\infty }\:(-1)^n \frac {1} {n^2}$$
Attempt:
I got this using Ratio Test: 
$$\lim_{n \to \infty} \frac{n^2}{(n+1)^2}$$

$\frac{1}{n^2}$ converges by the p-series test. Since $\frac{1}{n^2}$  is always decreasing as $n$ increases the alternating series $(-1)^n\frac{1}{n^2}$ also converges. Hence, it is absolutely convergent.
