Powerful Product

Calculus Level 5

n=0(122n+1122n+1)\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 AB\frac AB, where AA and BB are coprime positive integers. What is the value of A+B?A+B?

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