## Calculus 8th Edition

$\lim\limits_{k \to \infty} \frac {a_{k}}{b_{k}}=\lim\limits_{k \to \infty}\dfrac{\frac{\sqrt[3] {k}-1}{k(\sqrt k+1)}}{\frac{\sqrt[3] {k}}{k(\sqrt k)}}$ $=1\gt 0$ The given series converges by the LCT. Here, $b_{k}$ is a p-series and the series is convergent.