Chapter 5.6, Problem 358E

In the following exercises, use an appropriate test to determine whether the series converges.

358. $\begin{array}{l}{a}_k={\left(\frac{k}{k+\ln k}\right)}^k\\ a_k={\left(1+\frac{\ln k}{k}\right)}^{-\left(k/\ln k\right)\ln k}\approx e^{-\ln k.)}\end{array}$