Home Competitions RU-ALLRUSSIAN 1979 Problem 5
RU-ALLRUSSIAN 1979 Problem 5
The real sequence x 1 ≥ x 2 ≥ x 3 ≥ … \mathrm{x}_1\geq \mathrm{x}_2\geq \mathrm{x}_3\geq \ldots x 1 ≥ x 2 ≥ x 3 ≥ … x 1 + x 4 / 2 + x 9 / 3 + x 16 / 4 + … + x N / n ≤ 1 \mathrm{x}_1 + \mathrm{x}_4 / 2 + \mathrm{x}_9 / 3 + \mathrm{x}_{16} / 4 + \ldots +\mathrm{x}_\mathrm{N} / \mathrm{n}\leq 1 x 1 + x 4 /2 + x 9 /3 + x 16 /4 + … + x N / n ≤ 1 N = n 2 \mathrm{N} = \mathrm{n}^2 N = n 2 x 1 + x 2 / 2 + x 3 / 3 + … + x n / n ≤ 3 \mathrm{x}_1 + \mathrm{x}_2 / 2 + \mathrm{x}_3 / 3 + \ldots +\mathrm{x}_\mathrm{n} / \mathrm{n}\leq 3 x 1 + x 2 /2 + x 3 /3 + … + x n / n ≤ 3
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