Q110 / 225 · JEE Main 2004 · Mathematics

$\lim _{n \rightarrow \infty} \sum_{r=1}^n \frac{1}{n} e^{\frac{-}{n}}$ is

  • A
    e
  • Correct answer
    B
    $e-1$
  • C
    $1-e$
  • D
    $e+1$

Solution

$\lim _{n \rightarrow \infty} \sum_{r=1}^n \frac{1}{n} e^{\frac{r}{n}}=\int_0^1 e^x d x=(e-1)$

Hence, the correct answer is option: 'B'.

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