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Riemann Sums, Summation Notation, Definite Integral Notation

AP Calculus AB· difficulty 3/5

lim⁡n→∞∑i=1n1n(in)2=\displaystyle\lim_{n\to\infty}\sum_{i=1}^n \dfrac{1}{n}\left( \dfrac{i}{n}\right)^2 =

  • A

    14\tfrac{1}{4}

  • B

    12\tfrac{1}{2}

  • C

    13\tfrac{1}{3}

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  • D

    11

Explanation

Right-Riemann sum for ∫01x2 dx=1/3\int_0^1 x^2\,dx = 1/3.

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