Limit of Bunch of Powers of n
Source: HMMT 2008 Calculus Problem 9
March 2, 2008
limitintegrationHMMTlogarithmscalculusreal analysiscalculus computations
Problem Statement
(7) Evaluate the limit \lim_{n\rightarrow\infty}
n^{\minus{}\frac{1}{2}\left(1\plus{}\frac{1}{n}\right)}
\left(1^1\cdot2^2\cdot\cdots\cdot n^n\right)^{\frac{1}{n^2}}.