Answer
Convergent
Work Step by Step
$\lim\limits_{n \to \infty} \frac {a_{n}}{b_{n}}=\lim\limits_{n \to \infty}\frac{\frac{n-1}{n^{3}+1}}{1/n^{2}}$
$=\lim\limits_{n \to \infty}\frac{n^{3}-n^{2}}{n^{3}+1}$
$=\lim\limits_{n \to \infty}\frac{1-1/n}{1+1/n^{3}}$
$=1$
The given series converges by the LCT.