# Homework Help: (2n)!/(n^n) does the infinte series converge?

1. Dec 4, 2008

### heshbon

1. The problem statement, all variables and given/known data

Sorry for the missing summation signs but could anyone help me investigate the convergance of the following infinte sum with n'th term equal to : (2n)!/(n^n)

2. Relevant equations

3. The attempt at a solution

I have tried ratio test and n'th root test but failed.
Im not even sure if it passes the vanishing test

would appreciate any ideas. Thanks

2. Dec 4, 2008

### Dick

Use Stirling's approximation.

3. Dec 4, 2008

### sutupidmath

Well, using ratio test, i got that the limit goes to infinity, looks strange, but, i think that it diverges.

4. Dec 5, 2008

### heshbon

using sterlings equationm plus nth root test i get a limit which tends to infinity, but i think you can only conclude something about convergance of the sseries if the limit is real...

5. Dec 5, 2008

### Dick

For the series to converge the limit must be zero, right? It's not.