# Fermat Number Fractions

Calculus Level 3

Let $$F_n$$ denote the $$n^\text{th}$$ Fermat number, $$F_n = 2^{2^n} + 1$$. Find $\displaystyle \large \prod_{n=0}^\infty \left( 1 - \dfrac1{F_n} \right) .$

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