1 point) Use the ratio test to determine whether $\sum_{n=8}^{\infty} \frac{n(-5)^n}{n!}$ converges or diverges.
a) Find the ratio of successive terms. Write your answer as a fully simplified fraction. For $n \ge 8$,
$\lim_{n \to \infty} \left| \frac{a_{n+1}}{a_n} \right| = \lim_{n \to \infty}$
b) Evaluate the limit in the previous part. Enter $\infty$ as infinity and $-\infty$ as -infinity. If the limit does not exist, enter DNE.
$\lim_{n \to \infty} \left| \frac{a_{n+1}}{a_n} \right| =$
c) By the ratio test, does the series converge, diverge, or is the test inconclusive? Choose
