Answer
Divergent
Work Step by Step
$\lim\limits_{n \to \infty} \frac {a_{n}}{b_{n}}=\lim\limits_{n \to \infty}\frac{\frac{n^{2}-1}{n^{3}+1}}{1/n}$
$=\lim\limits_{n \to \infty}\frac{n^{3}-n}{n^{3}+1}$
$=\lim\limits_{n \to \infty}\frac{1-1/n^{2}}{1+1/n^{3}}$
$=1\ne 0\ne \infty$
The series is divergent.