Evaluate the limit _ n _ i=1 ^ n ( (2i-1) 2n )

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

Problem

Evaluate the limit

\lim_{n\to\infty}\sum_{i=1}^{n}\sin\left(\frac{\pi(2i-1)}{2n}\right)\,\frac{\pi}{n}.