[SOLVED] Infinite Series

[garryh22]

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

[Roberto Bramb]

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

[garryh22]

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