Use the ratio test to determine whether $\displaystyle \sum_{n=18}^{\infty} \frac{n+3}{n!}$ converges or diverges.

(a) Find the ratio of successive terms. Write your answer as a fully simplified fraction. For $n \geq 18$,

$\displaystyle \lim_{n \to \infty} \left| \frac{ a_{n+1} }{ a_{n} } \right| = \lim_{n \to \infty}$

(b) Evaluate the limit in the previous part. Enter $\infty$ as infinity and $-\infty$ as -infinity. If the limit does not exist, enter DNE.
$\displaystyle \lim_{n\to\infty} \left| \frac{a_{n+1}}{a_{n}} \right| \,$ =

(c) By the ratio test, does the series converge, diverge, or is the test inconclusive? Choose Converges Diverges Inconclusive