$\mathop {\lim }\limits_{n \to \infty } \,\,\frac{1}{n}\,\,\mathop \sum \limits_{r = 1}^n \,\,\frac{r}{{\sqrt {{n^2} + \,\,{r^2}} }}$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\lim\limits_{n \to \infty } \,\,\frac{1}{n}\,\,\sum \limits_{r = 1}^n \,\,\frac{r}{{\sqrt {{n^2} + \,\,{r^2}} }}

is equal to

View answer and explanation

Correct option: B

\sqrt 2 - 1

Option B (

\sqrt 2 - 1

) is correct because it is the result of converting the limit of the sum to a definite integral and evaluating it.

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