# Can I use the logic?

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

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## Answers and Replies

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