Is the alternating series $\sum_{n=1}^{\infty }(-1)^n \frac {n^2 - 1}{2n^2 + 3}$ divergent? I tried every test for convergence and really came up with nothing. Without answering the problem directly, is it possible to determine the divergence or convergence for this series?
$$\sum_{n=1}^{\infty }(-1)^n \frac {n^2 - 1}{2n^2 + 3}$$
If it can be determined could someone give a little hint as to what direction to take? Thank you!

Let
$$a_n=(-1)^n\frac{n^2-1}{2n^2+3}$$
we have $$\forall n\in \mathbb N^* \;\;
|a_n|=\frac{1-\frac{1}{n^2}}{2+\frac{3}{n^2}}$$
which yields to
$$\lim_{n\to +\infty}|a_n|=\frac{1}{2}$$
and
$$\lim_{n\to+\infty} a_n \neq 0$$
thus, the series $\sum a_n$ is divergent.
