Use the Root Test $to$ determine whether the series convergent $or$ divergent.

${\displaystyle \underset{n=1}{\overset{}{}}}(\frac{n^2+9}{9n^2+1}{)}^n$

Identify $a_n.$

Evaluate the following $limit.$

$\underset{n}{lim}\sqrt[n]{|a_n|}$

Since $\underset{n}{lim}\sqrt[n]{|a_n|}?vv1,$