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Compute the following limit $\lim_{n \to \infty} \sum_{k=1}^n \frac{1}{\sqrt{n^2+kn}}$

Please I need your help asap

Cheers

Matthew

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    $\lim_{x \to \infty} \frac{1}{\sqrt{n}} \sum{\frac{1}{\sqrt{n+k}}}$2012-11-06

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$\sum_{k=1}^n\frac{1}{\sqrt{n^2+kn}}=\frac{1}{n}\sum_{k=1}^n\frac{1}{\sqrt{1+\frac{k}{n}}}\xrightarrow [n\to\infty]{}\int_0^1\frac{dx}{\sqrt{1+x}}$

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    @Matthew That step considers your sum as a Riemann Sum for the given integral. If this is something you're unfamiliar with, it's worth looking up.2012-11-06