Titans86
Apr14-09, 10:59 PM
1. The problem statement, all variables and given/known data
I'm wondering if I can use this kind of logic to solve:
\sum\frac{(n+1)^n}{n^{(n+1)}} Converges or diverges
3. The attempt at a solution
\frac{(n+1)^n}{n^{(n+1)}} \geq \frac{(n)^n}{n^{(n+1)}}
And
\frac{(n)^n}{n^{(n+1)}} = n , which diverges
Therefor:
\sum\frac{(n+1)^n}{n^{(n+1)}} Diverges
I'm wondering if I can use this kind of logic to solve:
\sum\frac{(n+1)^n}{n^{(n+1)}} Converges or diverges
3. The attempt at a solution
\frac{(n+1)^n}{n^{(n+1)}} \geq \frac{(n)^n}{n^{(n+1)}}
And
\frac{(n)^n}{n^{(n+1)}} = n , which diverges
Therefor:
\sum\frac{(n+1)^n}{n^{(n+1)}} Diverges