# Thread: How to find whether this series converges or diverges

1. ## How to find whether this series converges or diverges

Problem: Determine whether the following series converges or diverges.

n! / (n^n)

I know that I need to find another function to compare it to, but I'm at a complete loss for one that will give me a finite limit (and easy to tell whether it is conv or div) or one that is always bigger and converges, or always smaller and diverges. Does anyone have any suggestions as to what I should use? Thank you.

2. Originally Posted by uberbandgeek6
Problem: Determine whether the following series converges or diverges.

n! / (n^n)

I know that I need to find another function to compare it to, but I'm at a complete loss for one that will give me a finite limit (and easy to tell whether it is conv or div) or one that is always bigger and converges, or always smaller and diverges. Does anyone have any suggestions as to what I should use? Thank you.
You call it a series so why not use the ratio test?

$\lim_{n\rightarrow\infty} \frac{(n+1)!}{(n+1)^{(n+1)}}\cdot \frac{n^n}{n!}$

3. Originally Posted by artvandalay11
You call it a series so why not use the ratio test?

$\lim_{n\rightarrow\infty} \frac{(n+1)!}{(n+1)^{(n+1)}}\cdot \frac{n^n}{n!}$
We haven't learned that yet in class, so I would probably get docked points for not using one of the strategies I listed above.