Chapter 9.4, Problem 29ES

Use the results of Exercises 27 and 28, if needed, to determine whether each series converges or diverges.

$\left(\text{a}\right){\displaystyle \underset{k=1}{\overset{\infty }{\sum }}\left[{\left(\frac{2}{3}\right)}^{k-1}+\frac{1}{k}\right]\left(\text{b}\right)}{\displaystyle \underset{k=1}{\overset{\infty }{\sum }}\left[\frac{1}{3k+2}-\frac{1}{k^{3/2}}\right]}$