HMMT November 2009 E10

Compute

$\prod_{n=0}^{\infty}\left(1-\left(\frac{1}{2}\right)^{3^{n}}+\left(\frac{1}{4}\right)^{3^{n}}\right)$

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

\frac{2}{3}

Solutions

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