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Riemann Sums, Summation Notation, Definite Integral Notation

AP Calculus AB· difficulty 3/5

lim⁡n→∞∑i=1n1n⋅ei/n\displaystyle\lim_{n\to\infty}\sum_{i=1}^n \dfrac{1}{n}\cdot e^{i/n} equals

  • A

    11

  • B

    00

  • C

    e−1e - 1

    check_circle
  • D

    ee

Explanation

Right Riemann sum on [0,1][0, 1] for f(x)=exf(x) = e^x. Limit =∫01ex dx=e−1= \int_0^1 e^x\,dx = e - 1.

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