## Calculus 8th Edition

$\Sigma_{k=1}^{\infty}\frac{k lnk }{(k+1)^{3}}$ We note that $\sqrt k \gt lnk$ Then $\frac{\sqrt k}{k^{2}}=\frac{1}{k^{3/2}}$ As a series $\Sigma_{k=1}^{\infty}\frac{1}{k^{3/2}}$ converges because it is a p-series with $p=\frac{3}{2}\gt 1$