# Powers of 1/2

Algebra Level 2

$S = \frac {1}{2^1} + \frac {1}{2^2} + \frac {1}{2^3} + \ldots + \frac {1}{2^7}.$

If $$S = \frac {a}{b}$$, where $$a$$ and $$b$$ are positive, coprime numbers, what is the value of $$a+b$$?

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