Answer
The series is absolutely convergent.
Work Step by Step
Ratio Test: $\lim\limits_{n \to \infty}|\dfrac{a_{n+1}}{a_{n}}|=\lim\limits_{n \to \infty}|\dfrac{\frac{(-3)^{n+1}}{(2n+3)!}}{\frac{(-3)^{n}}{(2n+1)!}}|$
$=\lim\limits_{n \to \infty}|\frac{3}{(2n+2)((2n+3)}|$
$=0\lt 1$
The series is absolutely convergent.