JEE MATHEMATICS MCQ: LIMITS

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\lim\limits_{x \to \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}}}} }} + .... + \frac{1}{{\sqrt {1 - \frac{{{2^n} - 1}}{{{2^n}}}} }}} \right)

is equal to

View answer and explanation

Correct option: C

Option C (2) is correct. The limit is evaluated by converting the sum to an integral and then evaluating the integral.

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