Determine the value of the constant if _ n _ i=1 ^ n (k (1+ 2i n )^ 2 ) 2 n =24.

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

Problem

Determine the value of the constant kk if lim⁡n→∞∑i=1n(k(1+2in)2)⋅2n=24.\lim_{n\to\infty}\sum_{i=1}^{n}\left(k\Bigl(1+\tfrac{2i}{n}\Bigr)^{2}\right)\cdot\tfrac{2}{n}=24.

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