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$$\lim_{n\to\infty}\left(\frac{1}{n}\sum_{i=0}^{n} \sqrt{\frac{i}{n}}\right)$$Any tips how to solve this problem, because clearly I have no idea how to approach it.

Clayton
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Peter Yang
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    See http://math.stackexchange.com/questions/469885/the-limit-of-a-sum-sum-k-1n-fracnn2k2?lq=1 OR http://math.stackexchange.com/questions/465075/find-lim-limits-n-to-infty-frac1n-sum-limits2n-r-1-fracr-sq – lab bhattacharjee Sep 04 '15 at 13:05
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    http://math.stackexchange.com/questions/805693/find-lim-n-rightarrow-infty-sum-k-1-n-frac-sqrt-k?rq=1 – Noam Shalev - nospoon Sep 04 '15 at 13:13

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Hint: This is a Riemann Sum

$$\lim_{n \to \infty} \frac{1}{n} \sum _{i=0}^{n} \sqrt{\frac{i}{n}} = \int_0^1 \sqrt x\, dx =\frac{2}{3}.$$

Jack D'Aurizio
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Aaron Maroja
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