## Calculus 8th Edition

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