(2n)/(n^n) does the infinte series converge?

[heshbon]

Homework Statement

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

Homework Equations

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

 

[Dick]

Use Stirling's approximation.

 

[sutupidmath]

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

 

[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...

 

[Dick]

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