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## Homework Statement

Determine whether or not the series [tex]\sum^{\infty}_{n=1} \frac{1}{\sqrt{n+1}+\sqrt{n}}[/tex] converges.

## The Attempt at a Solution

Assuming this diverges, I rationalize it to get get [tex]\sum^{\infty}_{n=1} \sqrt{n+1} - \sqrt{n}[/tex]. How would I proceed further?

Is this even the right approach?