Chapter 9.4, Problem 6ES

Apply the divergence test and state what it tells you about the series.

$\begin{array}{l}\left(\text{a}\right){\displaystyle \underset{k=1}{\overset{\infty }{\sum }}\frac{k}{e^k}}\left(\text{b}\right){\displaystyle \underset{k=1}{\overset{\infty }{\sum }}\ln k}\\ \left(\text{c}\right){\displaystyle \underset{k=1}{\overset{\infty }{\sum }}\frac{1}{\sqrt{k}}}\left(\text{d}\right){\displaystyle \underset{k=1}{\overset{\infty }{\sum }}\frac{\sqrt{k}}{\sqrt{k}+3}}\end{array}$