# Powerful Product

Calculus Level 4

$\large\prod _{n=0}^\infty\left(\frac1{2^{2^{n+1}}}-\frac1{2^{2^n}}+1\right)$ The above infinite product can be written as $$\dfrac AB$$, where $$A$$ and $$B$$ are coprime positive integers. What is the value of $$A+B$$?

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