How can I calculate the sum of these roots? – math.stackexchange.com

How can I calculate the sum of these roots? – math.stackexchange.com

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My math prof has proposed this question in class during a combinatorics lesson. $$\sum_{n=1}^{10^6}\lfloor\sqrt n\rfloor$$ Her hint is that: $$\sum_{i=1}^ki^2=\frac{k(k+1)(2k+1)}6$$

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