Solving Sum of n+1^n/n^(n+1) - Diverges?

[Titans86]

Can I use this logic?

Homework Statement

I'm wondering if I can use this kind of logic to solve:

$$\sum\frac{(n+1)^n}{n^{(n+1)}}$$ Converges or diverges

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

 

[whybother]

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