Chapter 9, Problem 16RE

Use any method to determine whether the series converge.

$\begin{array}{l}\text{(a)}{\displaystyle \underset{k=1}{\overset{\infty }{\sum }}{(-1)}^k\frac{k+4}{k^2+k}}\\ \text{(b)}{\displaystyle \underset{k=1}{\overset{\infty }{\sum }}(}-1{)}^{k+1}{\left(\frac{k+2}{3k-1}\right)}^k\end{array}$