A sum

Calculus Level 2

∑n=1∞22n−122n+1=ab\large \sum_{n=1}^{\infty} \frac{2^{2^{n}}-1}{2^{2^{n+1}}} = \frac ab

If the equation above holds true for coprime positive integers aa and bb, find the value of a+ba+b.

Freddie Hand by Freddie Hand
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