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**Can I use this logic?**

## Homework Statement

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

[tex]\sum\frac{(n+1)^n}{n^{(n+1)}}[/tex] Converges or diverges

## The Attempt at a Solution

[tex] \frac{(n+1)^n}{n^{(n+1)}} \geq \frac{(n)^n}{n^{(n+1)}} [/tex]

And

[tex] \frac{(n)^n}{n^{(n+1)}} = n [/tex] , which diverges

Therefor:

[tex]\sum\frac{(n+1)^n}{n^{(n+1)}}[/tex] Diverges

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