The two limits _ n _ i=1 ^ n (A (2+ 2i n )+B ) 2 n =30 and _ n _ i=1 ^ n (A (2+ i n…

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

Problem

The two limits

\lim_{n\to\infty}\sum_{i=1}^{n}\bigl(A\bigl(2+\tfrac{2i}{n}\bigr)+B\bigr)\cdot\tfrac{2}{n}=30\quad\text{and}\quad\lim_{n\to\infty}\sum_{i=1}^{n}\bigl(A\bigl(2+\tfrac{i}{n}\bigr)+B\bigr)\cdot\tfrac{1}{n}=12

are both finite. Determine the ordered pair

(A,B)