$\mathop {\lim }\limits_{n \to \infty } \,\,\frac{1}{{{n^2}}}\,\,\mathop \sum \limits_{r = 1}^n \,\,r\;{e^{r/n}} = $

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\lim\limits_{n \to \infty } \,\,\frac{1}{{{n^2}}}\,\,\sum \limits_{r = 1}^n \,\,r\;{e^{r/n}} =

View answer and explanation

Correct option: B

\mathrm{1}

The correct answer is B (1) because the limit of the Riemann sum can be evaluated as a definite integral, which equals 1 after integration by parts.

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