VWO 1993 Problem 4

Define the sequence $oa_n$ as follows: $oa_0=1, oa_n= oa_{n-1} \cdot cos\left( \dfrac{\pi}{2^{n+1}} \right)$ .

Find $\lim\limits_{n\rightarrow+\infty} oa_n$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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