Chapter 8.4, Problem 59PS

To determine

To show: that the series ${\displaystyle \sum a_k}$ converges whenever ${\displaystyle \sum b_k}$ converges provided $a_k>0,b_k>0$ for all $k$ and $\underset{k\to \infty }{\lim }\frac{a_k}{b_k}=0$ .