Evaluate the limit _ n _ i=1 ^ n (1+ 3i n )^ 2 , 3 n .

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

Problem

Evaluate the limit lim⁡n→∞∑i=1n(1+3in)2 3n.\lim_{n\to\infty}\sum_{i=1}^{n}\left(1+\frac{3i}{n}\right)^{2}\,\frac{3}{n}.

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