Consider the series ∑n=1∞n!annn\sum_{n=1}^{\infty} \frac{n!}{a^n n^n}∑n=1∞annnn! for a>0a > 0a>0. For which values of aaa does this series converge?
a>1/ea > 1/ea>1/e
a>ea > ea>e
a>1a > 1a>1
a>e2a > e^2a>e2