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Infinite Series

  1. Apr 8, 2008 #1
    [SOLVED] Infinite Series

    1. The problem statement, all variables and given/known data

    ln((n!e^n)/n^(n+1/2))

    2. Relevant equations

    Does the series above converge or diverge.

    3. The attempt at a solution

    I can see that it diverges but I'm looking for the appropriate test to show this
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 8, 2008 #2
    The series is convergent by Cauchy criterium since C(n+1)/C(n)->0 for n>infinity,
    as can be easily verified using Striling formula : log(n!) => n*log(n)-n
     
  4. Apr 8, 2008 #3
    Thanks a great deal. I never heard of the Striling formula till now. I just looked it up, applied it and the expression reduced to ln(1/n)^(1/2) which diverges with p-series. Further insight would be greatly appreciated
     
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