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(2n)!/(n^n) does the infinte series converge?

  1. Dec 4, 2008 #1
    1. The problem statement, all variables and given/known data

    Sorry for the missing summation signs but could anyone help me investigate the convergance of the following infinte sum with n'th term equal to : (2n)!/(n^n)

    2. Relevant equations

    3. The attempt at a solution

    I have tried ratio test and n'th root test but failed.
    Im not even sure if it passes the vanishing test

    would appreciate any ideas. Thanks
  2. jcsd
  3. Dec 4, 2008 #2


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    Use Stirling's approximation.
  4. Dec 4, 2008 #3
    Well, using ratio test, i got that the limit goes to infinity, looks strange, but, i think that it diverges.
  5. Dec 5, 2008 #4
    using sterlings equationm plus nth root test i get a limit which tends to infinity, but i think you can only conclude something about convergance of the sseries if the limit is real...
  6. Dec 5, 2008 #5


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    For the series to converge the limit must be zero, right? It's not.
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