# Can I use the logic?

1. Apr 14, 2009

### Titans86

Can I use this logic?

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

Last edited: Apr 15, 2009
2. Apr 14, 2009

### whybother

Yes. So long as it's true for all n and n > 0.