374

Part of 2008 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 374

Source: 1996 Osaka University entrance exam/Science

n\geq 2

be positive integers. (1) Prove that n\ln n \minus{} n\plus{}1<\sum_{k\equal{}1}^n \ln k<(n\plus{}1)\ln n \minus{} n\plus{}1. (2) Find

\lim_{n\to\infty} (n!)^{\frac{1}{n\ln n}}

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