Answer
Absolutely convergent
Work Step by Step
By Ratio Test, we have
$\lim_{n\to\infty}\biggl| \frac{9^{n+1}}{(n+1)10^{n+2}}\frac{n10^{n+1}}{9^n}\biggr|=\lim_{n\to\infty}\biggl|\frac{9}{10}\frac{n}{n+1}\biggr|=\frac{9}{10}$
Since the limit $ < 1$, the series is absolutely convergent by Ratio Test
