Chapter 9.4, Problem 1ES

Use Theorem 9.4.3 to find the sum of each series.

$\begin{array}{l}\left(\text{a}\right)\left(\frac{1}{2}+\frac{1}{4}\right)+\left(\frac{1}{2^2}+\frac{1}{4^2}\right)+\cdot \cdot \cdot +\left(\frac{1}{2^k}+\frac{1}{4^k}\right)+\cdot \cdot \cdot \\ \left(\text{b}\right){\displaystyle \underset{k=1}{\overset{\infty }{\sum }}\left(\frac{1}{5^k}-\frac{1}{k\left(k+1\right)}\right)}\end{array}$