Today's calculation of Integral 348
Source: 2008 Toyama University entrance exam/Medical, Pharmacy
June 20, 2008
calculusintegrationlimitlogarithmscalculus computations
Problem Statement
Find \lim_{n\to\infty} \left(\frac{n\plus{}1}{n}\right)^{\frac{1}{n^2}}\left(\frac{n\plus{}2}{n}\right)^{\frac{2}{n^2}}\left(\frac{n\plus{}3}{n}\right)^{\frac{3}{n^2}}\cdots \left(\frac{n\plus{}n}{n}\right)^{\frac{n}{n^2}}\ (n\equal{}1,\ 2,\ 3,\ \cdots).