Answer
Absolutely comvergent
Work Step by Step
$a_n=(\frac{1-n}{2+3n})^n$
$|a_{n}| = \biggl|(\frac{1-n}{2+3n})^n\biggr|$
By Root Test, we get
$\lim_{n\to\infty}\sqrt[n]{|a_n|}=\lim_{n\to\infty}\biggl|\frac{1-n}{2+3n}\biggr|=\biggl|-\frac{1}{3}\biggr|=\frac{1}{3}$
Since the limit $ < 1 $, the series is absolutely convergent