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

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}^{2n} \,\,\frac{r}{{\sqrt {{n^2} + {r^2}} }}

equals

View answer and explanation

Correct option: B

- 1 + \sqrt 5

Option B (

- 1 + \sqrt 5

) is correct because the limit of the Riemann sum can be expressed as a definite integral, which evaluates to

-1 + \sqrt{5}

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