Chapter 5.4, Problem 239E

Use the limit comparison test to determine whether each of the following series converges or diverges.

239. Show that if

$a_n\ge 0$ and ${\displaystyle \underset{n=1}{\overset{\infty }{\sum }}{a}^{2}n}$ converges, then

   ${\displaystyle \underset{n=1}{\overset{\infty }{\sum }}{\sin }^2\left(a_n\right)}$ converges.