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## Homework Statement

Let [tex]y_n := \sqrt{n+1} - \sqrt{n}[/tex] for [tex]n \in \mathbb{N}[/tex]. Show that [tex] (y_n)[/tex] converges.

## Homework Equations

## The Attempt at a Solution

I see that it converges to 0. I just need a nudge in the right direction at getting into [tex]| \sqrt{n+1} - \sqrt{n} - 0 | = | \sqrt{n+1} - \sqrt{n} |[/tex] to show it's less than any [tex]\epsilon > 0[/tex]. Any manipulating I've tried so far makes the terms way too big to work with.

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