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RU-ALLRUSSIAN 1987 Problem 22

    Show that (2n+1)n≥(2n)n+(2n−1)n(2\mathrm{n} + 1)^{\mathrm{n}}\geq (2\mathrm{n})^{\mathrm{n}} + (2\mathrm{n} - 1)^{\mathrm{n}} for every positive integer n.

    Dataset text NuminaMath olympiads. Quoted with source.

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