Problem

For

n \in \mathbb{N}

, let

f_n(x) = \tan \frac{x}{2} (1 + \sec x)(1 + \sec 2x)(1 + \sec 4x) \dots (1 + \sec 2^n x)

. Then,

\lim_{x \to 0} \frac{f_n(x)}{2x}

is a. 0 b.

2^n

2^{n-1}

2^{n+1}