Challenge for the Weak 2 - P3
Contributed by: cauchy
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Difficulty: 9
This problem is tagged with cw, cw2.
Consider the following product:
$$
p_n = \prod_{k=1}^{n} \cos(2^{k-1}x), \quad x \neq k\pi.
$$
Find the limit:
$$
\lim_{n \to \infty} p_n
$$
A. $1$
B. $\frac{\cos{x}}{x}$
C. $0$
D. $\frac{\sin{x}}{x}$
E. does not exist
Your answer should be a single capitalized letter, e.g., 'A'.
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