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Today's calculation of Integral 746

Source: 2011 Mie University entrance exam

August 29, 2011
calculusintegrationfloor functioninequalitiescalculus computations

Problem Statement

Prove the following inequality. nne−n+1≤n!≤14(n+1)n+1e−n+1.n^ne^{-n+1}\leq n!\leq \frac 14(n+1)^{n+1}e^{-n+1}.
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