Testing convergence of this series

[dangerman77]

The combination of the factorial and the exponent leads me to think its warrants the Ratio Test...but hmmm...

 

[royhaas]

Try it. It's actually easy.

 

[galactus]

Yes, you can use the ratio test.

\(\displaystyle \lim_{n\to\infty}\frac{(n+1)!}{(n+1)^{n+1}}\frac{n^{n}}{n!}\)

You'll find this limit converges to something finite.

You can also use the root test.