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Infinite Series

  • Thread starter garryh22
  • Start date
4
0
[SOLVED] Infinite Series

1. Homework Statement

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

2. Homework 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. Homework Statement



2. Homework Equations



3. The Attempt at a Solution
 

Answers and Replies

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
0
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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