Infinite Series Convergence/Divergence

[curtissc]

Homework Statement

Test the series for convergence or divergence

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

Homework Equations

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

The Attempt at a Solution

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

 

[Bohrok]

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

 

[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.