Chapter 9, Problem 19RE

Use any method to determine whether the series converge.

$\begin{array}{l}\text{(a)}{\displaystyle \underset{k=1}{\overset{\infty }{\sum }}\frac{9}{\sqrt{k}+1}}\\ \text{(b)}{\displaystyle \underset{k=1}{\overset{\infty }{\sum }}\frac{\cos (1/k)}{k^2}}\end{array}$