Convergence of $ \sum_{n=1}^\infty\frac{e^nn!}{n^n} $

Question

Is the following series convergent? $$ \sum_{n=1}^\infty\frac{e^nn!}{n^n} $$

score 3 · Accepted Answer · edited Apr 13 '17 at 12:20

3

HINT

$$n! >(\frac{n}{e})^n$$

From here.

edited Apr 13 '17 at 12:20

Community

answered Mar 14 '16 at 06:53

S.C.B.

1 Answers1