Rewrite the limit _ n _ k=1 ^ n ! (1+ 2k n ) 2 n as a single definite integral in

MATHEMATICS · Subjective · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Rewrite the limit

\lim_{n\to\infty}\sum_{k=1}^{n}\ln\!\left(1+\frac{2k}{n}\right)\frac{2}{n}

as a single definite integral in

x

. Do not evaluate the integral.