Evaluate the limit _ n [ , 1 n _ i=1 ^ n i n + 1 n _ i=n+1 ^ 2n 3 , ].

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

Problem

Evaluate the limit

\lim_{n\to\infty}\left[\,\frac{1}{n}\sum_{i=1}^{n}\frac{i}{n}+\frac{1}{n}\sum_{i=n+1}^{2n}3\,\right].