Saturday, October 10, 2015

real analysis - compute $lim_{nto infty} sqrt{n}(sqrt{n+1}-sqrt{n})$











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


Answer



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


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