Unlimited Sigma

Calculus Level 3

lim ⁡ n → ∞ ∑ r = 1 n 3 ( 1 + r n ) 2 1 n = ? \large \lim \limits_{n \to \infty} \displaystyle \sum_{r=1}^ n 3\left(1+\dfrac{r}{n} \right)^2 \dfrac{1}{n} = \ ?


The answer is 7.

Anish Harsha by Anish Harsha , 20, India

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1 solution

Otto Bretscher
Nov 11, 2015

It's the right Riemann sum of 3 x 2 3x^2 on [ 1 , 2 ] [1,2] . so that the limit is ∫ 1 2 3 x 2 d x = 7 \int_{1}^{2}3x^2dx=\boxed{7}

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