- #1
v0id19
- 49
- 0
Homework Statement
Determine whether the series [tex]\sum_{n=1}^{\infty}{\frac{n!}{n^n}}[/tex] converges or diverges.
Homework Equations
The Comparison Test
The Limit Comparison Test
The Attempt at a Solution
I know it diverges, and i tried [tex]a_n=\frac{n!}{n^n}[/tex] and [tex]b_n=\frac{1}{n^n}[/tex] for the limit comparison test, but it gave me infinity which is useless. I also tried the comparison test saying [tex]a_n=\frac{n!}{n^n} \ge b_n=\frac{1}{n^n}[/tex] but i don't know how to prove that [tex]\frac{1}{n^n}[/tex] diverges