The value of is:

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

The value of

\lim_{n\to\infty}n^{-n^2}\left[(n+1)\left(n+\frac12\right)\left(n+\frac1{2^2}\right)\cdots\left(n+\frac1{2^{n-1}}\right)\right]^n

is: (1)

e

(2)

e^2

(3)

e^3

(4)

e^4