Infinite Series Convergence/Divergence

1. Apr 5, 2010

curtissc

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

Test the series for convergence or divergence

$$\sum$$$$^{\infty}_{1}$$ $$\frac{(n!)^{n}}{n^{4n}}$$

2. Relevant equations

Ratio test seems likely since it contains n!, but I think I'm missing something

3. The attempt at a solution

After a failed attempt to use Ratio Test, I'm lost...

2. Apr 5, 2010

Bohrok

Can you show whether n!/n4 goes to 0 as n→∞ first?

3. Apr 10, 2010

Whitishcube

maybe use the nth root test? i see both of those terms have a power of n, so i think nth root test. could be wrong though.