Answer
The series diverges
Work Step by Step
let $b_{n}$ = $\frac{n^2}{n^2+1}$
Taking the limit of n goes to infinity:
$\lim\limits_{n \to \infty}$ $\frac{n^2}{n^2+1}$ =
$\lim\limits_{n \to \infty}$ $\frac{1}{1+1/n^2}$ =
$\lim\limits_{n \to \infty}$ $\frac{1}{1 + 0 }$ = 1 $\ne$ 0
SO by alternating series test, the original series diverges
