IT-CESENATICO 1998 Problem 1

Calculate the sum $\sum_{n=1}^{1.000.000}[ \sqrt{n} ]$ .

You may use the formula $\sum_{i=1}^{k} i^2=\frac{k(k +1)(2k +1)}{6}$ without a proof.

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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