1. Apr 5, 2010 #1

   curtissc

   

   1. The problem statement, all variables and given/known data
   
   Test the series for convergence or divergence
   
   [tex]\sum[/tex][tex]^{\infty}_{1}[/tex] [tex]\frac{(n!)^{n}}{n^{4n}}[/tex]
   
   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...

    

   curtissc, Apr 5, 2010
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3. Apr 5, 2010 #2

   Bohrok

   

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

    

   Bohrok, Apr 5, 2010
4. Apr 10, 2010 #3

   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.

    

   Whitishcube, Apr 10, 2010

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