Chapter 8.3, Problem 59PS

To determine

To show: if ${\displaystyle \sum a_k}$ converges, then ${\displaystyle \underset{1}{\overset{\infty }{\int }}f\left(k\right)dx\le {\displaystyle \sum _{k=1}^{\infty }{a}_k\le a_1}}+{\displaystyle \underset{1}{\overset{\infty }{\int }}f\left(k\right)dx}$