AP

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

\lim_{n\to\infty}n^{-\frac{1}{2}\left(1+\frac{1}{n}\right)}\left(1^1\cdot2^2\cdot3^3\cdots n^n\right)^{\frac{1}{n^2}}

is equal to (1)

\sqrt{e}

(2)

\frac{1}{\sqrt{e}}

(3)

\frac{1}{\sqrt[4]{e}}

(4)

\sqrt[4]{e}