jee-main 2022 Q74

jee-main · India · session2_25jul_shift2 Indefinite & Definite Integrals Definite Integral as a Limit of Riemann Sums

$\lim_{n \rightarrow \infty} \frac{1}{2^n} \left( \frac{1}{\sqrt{1 - \frac{1}{2^n}}} + \frac{1}{\sqrt{1 - \frac{2}{2^n}}} + \frac{1}{\sqrt{1 - \frac{3}{2^n}}} + \ldots + \frac{1}{\sqrt{1 - \frac{2^n - 1}{2^n}}} \right)$ is equal to
(1) $\frac{1}{2}$
(2) 1
(3) 2
(4) $-2$

$\lim_{n \rightarrow \infty} \frac{1}{2^n} \left( \frac{1}{\sqrt{1 - \frac{1}{2^n}}} + \frac{1}{\sqrt{1 - \frac{2}{2^n}}} + \frac{1}{\sqrt{1 - \frac{3}{2^n}}} + \ldots + \frac{1}{\sqrt{1 - \frac{2^n - 1}{2^n}}} \right)$ is equal to\\
(1) $\frac{1}{2}$\\
(2) 1\\
(3) 2\\
(4) $-2$

Paper Questions

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