## Calculus 8th Edition

The Comparison Test states that the p-series $\sum_{n=1}^{\infty}\frac{1}{n^{p}}$ is convergent if $p\gt 1$ and divergent if $p\leq 1$. $\Sigma_{k=1}^{\infty} \frac{ksin^{2}k}{1+k^{3}}\geq \Sigma_{k=1}^{\infty} \frac{k}{1+k^{3}} \lt \Sigma_{k=1}^{\infty} \frac{k}{k^{3}}$ This is a p-series with $p =2 \gt 1$ . And we know that a series less than converging series is also converging.