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Infinite Series Convergence/Divergence

  1. Apr 5, 2010 #1
    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

    :confused: After a failed attempt to use Ratio Test, I'm lost...
  2. jcsd
  3. Apr 5, 2010 #2
    Can you show whether n!/n4 goes to 0 as n→∞ first?
  4. Apr 10, 2010 #3
    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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