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Today's calculation of Integral 219

Source: Kochi University entrance exam/Medical 2007

August 28, 2007
calculusintegrationlimitalgebrafunctiondomainlogarithms

Problem Statement

Let f(x)\equal{}\left(1\plus{}\frac{1}{x}\right)^{x}\ (x>0). Find lim⁡n→∞{f(1n)f(2n)f(3n)⋯⋯f(nn)}1n \lim_{n\to\infty}\left\{f\left(\frac{1}{n}\right)f\left(\frac{2}{n}\right)f\left(\frac{3}{n}\right)\cdots\cdots f\left(\frac{n}{n}\right)\right\}^{\frac{1}{n}}.
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