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A6

Part of 1949 Putnam

Problems(1)

Putnam 1949 A6

Source: Putnam 1949

3/20/2022
Prove that for every real or complex xx ∏k=1∞1+2cos⁡2x3k3=sin⁡xx.\prod_{k=1}^{\infty} \frac{1+2\cos \frac{2x}{3^{k}}}{3} =\frac{\sin x}{x}.
Putnamtrigonometry