Infinite Series Convergence/Divergence

curtissc
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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



:confused: After a failed attempt to use Ratio Test, I'm lost...
 
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Can you show whether n!/n4 goes to 0 as n→∞ first?
 
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.
 

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