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What is
\[
\lim _{n \rightarrow \infty} \cos \frac{\pi}{2^{2}} \cos \frac{\pi}{2^{3}} \cdots \cos \frac{\pi}{2^{n}} ?
\]

  1. $0$
  2. $\pi / 2$
  3. $1 / \sqrt{2}$
  4. $2 / \pi$
  5. None of the above.
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