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IMO Long List 1986 inequality for x_i

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August 29, 2010
algebraSequenceInequalitycalculusrecurrence relationIMO Shortlistinequalities

Problem Statement

Let xn=2+3+⋯+nn32.x_n = \sqrt[2]{2+\sqrt[3]{3+\cdots+\sqrt[n]{n}}}. Prove that x_{n+1}-x_n <\frac{1}{n!}   n=2,3,\cdots
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