_ n _ r = 1 ^n 1 n e^ r n is - Vidyadip

MCQ

$\mathop {\lim }\limits_{n \to \infty } \sum\limits_{r = 1}^n {\frac{1}{n}{e^{\frac{r}{n}}}} $ is

A
$e + 1$
✓
$e - 1$
C
$1 - e$
D
$e$

✓

Answer

Correct option: B.

$e - 1$

b
(b) $\mathop {\lim }\limits_{n \to \infty } \sum\limits_{r = 1}^n {\frac{1}{n}{e^{\frac{r}{n}}} = \int_0^1 {{e^x}dx = [{e^x}]_0^1 = e - 1} } $.

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