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How do I find the value of such ridiculous-looking sum?

$$\sum^{100}_{i=1}\lfloor \sqrt{i}\rfloor$$

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For a given $x$, how many $i \in \mathbb N$ are there such that $\lfloor\sqrt i\rfloor = x$? –  Peter Taylor Sep 26 '13 at 7:29
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Start calculating. There is a nice pattern. –  André Nicolas Sep 26 '13 at 7:29
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1 Answer

up vote 5 down vote accepted

Hint: Think about how many values $i$ starting from $1$ such that $1\leq\sqrt{i}<2$, then $2\leq\sqrt{i}<3$, so on until $9\leq\sqrt{i}<10$. This should help you get started.

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