lim n → ∞ ∑ r = 1 n n 1 e n − is, e, e − 1, 1 − e, e + 1

lim n → ∞ ∑ r = 1 n n 1 e n r = ∫ 0 1 e x d x = ( e − 1 )

lim n → ∞ ∑ r = 1 n n 1 e n − is

Question: Answered & Verified by Expert

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

MathematicsLimitsJEE MainJEE Main 2004

Options:

Solution:

2284 Upvotes Verified Answer

The correct answer is:
$e-1$

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

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