Consider the series ∑n=1∞n!an\sum_{n=1}^{\infty} \frac{n!}{a^n}∑n=1∞ann! for a>0a > 0a>0. For which aaa does it converge?
Never converges
Converges for a>1a > 1a>1
Converges for a>ea > ea>e
Only for a=∞a = \inftya=∞