(1 point) Consider the series $\sum_{n=1}^{\infty} a_n$ where $a_n = \frac{n^3(n+3)!}{n!2^{7n}}$.
Compute the limit:
$\lim_{n\to\infty} \frac{a_{n+1}}{a_n} = $
(Enter "infinity" or "inf" if the limit is infinity; enter "DNE" if the limit does not exist for another reason.)
Given your answer above, what does the ratio test tell you about the series?
