Chapter 9.4, Problem 30ES

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

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