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

${\displaystyle \underset{n=1}{\overset{}{}}}(\frac{n^2+9}{7n^2+8}{)}^n$

Identify $a_n.$

Evaluate the following limit$.$

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

Since $\underset{n}{lim}\sqrt[n]{|a_n|}1$