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Possible Duplicate:
Limits: How to evaluate $\lim\limits_{x\rightarrow \infty}\sqrt[n]{x^{n}+a_{n-1}x^{n-1}+\cdots+a_{0}}-x$
Calculate $\displaystyle\lim_{n\to{+}\infty}{(\sqrt{n^{2}+n}-n)}$

how should I approach the following limit? $\lim_{n\to \infty} \sqrt{n}(\sqrt{n+1}-\sqrt{n})$

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    This is the same limit as here: [Calculate $\displaystyle\lim_{n\to{+}\infty}{(\sqrt{n^{2}+n}-n)}$](http://math.stackexchange.com/questions/136495/calculate-displaystyle-lim-n-to-infty-sqrtn2n-n)2012-10-24

1 Answers 1

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A start: Multiply by $\dfrac{\sqrt{n+1}+\sqrt{n}}{\sqrt{n+1}+\sqrt{n}}$.

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    @Badshah: I try to discourage this kind of informal use of "$\infty$," since I have seen too many mistaken calculations that this can lead to.2012-10-24