Determine if the series $sum_{n=1}^{infty} frac{9^n}{(2n)!}$ converges or diverges.
(a) Find the ratio of successive terms. Write your answer as a fully simplified fraction. For $n ge 1$,
$lim_{n o infty} frac{a_{n+1}}{a_n} = lim_{n o infty}$
(b) Evaluate the limit in the previous part. Enter $infty$ as infinity and $-infty$ as -infinity. If the limit does not exist, enter DNE:
$lim_{n o infty} frac{a_{n+1}}{a_n} =$
(c) By the ratio test, does the series converge, diverge, or is the test inconclusive? Choose