Does the series converge or diverge?

${\displaystyle \underset{n=0}{\overset{}{}}}(-1{)}^{n+1}\frac{9^{n-1}}{(3+4n)!}$

If we use the Ratio Test, we need to find $\underset{n}{lim}|\frac{a_n+1}{a_n}|.$ What is $a_n?$

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Find $\underset{n}{lim}|\frac{a_{n+1}}{a_n}|.$

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Since $\underset{n}{lim}|\frac{a_{n+1}}{a_n}|?vv1,$