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I would like to know how to prove the following assertion :

For every $n>0$: $$\sqrt{n}+\frac{1}{\sqrt{n+1}} \geq \sqrt{n+1}$$

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    $$ \sqrt{n}+ \frac{1}{\sqrt{n+1}} \ge \sqrt{n+1} \\ \sqrt{n + 1}\sqrt{n} + 1 \ge n+1 \\ \sqrt{n + 1}\sqrt{n} \ge n \\ \sqrt{n + 1}\sqrt{n} \ge \sqrt{n}\sqrt{n} \\ \sqrt{n + 1}\sqrt{n} \ge \sqrt{n}\sqrt{n} \\ \sqrt{n + 1} \ge \sqrt{n} \\ $$2012-08-05
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    @J.D.: Why not an answer?2012-08-05

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