Chapter 9.4, Problem 5ES

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

$\begin{array}{l}\left(\text{a}\right){\displaystyle \underset{k=1}{\overset{\infty }{\sum }}\frac{k^2+k+3}{2k^2+1}}\left(\text{b}\right){\displaystyle \underset{k=1}{\overset{\infty }{\sum }}{\left(1+\frac{1}{k}\right)}^k}\\ \left(\text{c}\right){\displaystyle \underset{k=1}{\overset{\infty }{\sum }}\cos k\pi }\left(\text{d}\right){\displaystyle \underset{k=1}{\overset{\infty }{\sum }}\frac{1}{k!}}\end{array}$