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Question

Mathematics Question on Definite Integral

\lim_{n \to\infty} n^{-nk} \left\\{\left(n+1\right) \left(n+ \frac{1}{2}\right) \left(n + \frac{1}{2^{2}}\right) ...\left(n + \frac{1}{2^{k-1}}\right)\right\\}^{n} =

A

2

B

e2(1−12k)e^{2 \left(1- \frac{1}{2^{k}}\right)}

C

2(1−12k)2\left(1- \frac{1}{2^{k}}\right)

D

e2e^2

Answer

e2(1−12k)e^{2 \left(1- \frac{1}{2^{k}}\right)}

Explanation

Solution

Answer (b) e2(1−12k)e^{2 \left(1- \frac{1}{2^{k}}\right)}