Chapter 1.9, Problem 21P

Test the following series for convergence or divergence. Decide for yourself which test is easiest to use, but don’t forget the preliminary test. Use the facts stated above when they apply.

${\displaystyle \underset{n=1}{\overset{\infty }{\sum }}if{a}_{n+1}=\frac{n}{2n+3}}{a}_n$