Chapter 9 - Infinite Series - 9.2 Exercises - Page 601: 10

The series diverges

$if\lim _{n\rightarrow \infty }a_{n}\neq 0\Rightarrow \sum ^{n}_{1}a_{n}$ diverges $\lim _{n\rightarrow \infty }\dfrac {\eta }{2n+3}=\dfrac {n/n}{2n/n+3/n}=\dfrac {1}{2+\dfrac {3}{n}}=\dfrac {1}{2}\neq 0$ So the series diverges