Sum of Weird Fractions

Algebra Level 3

\[ \large \frac{1}{4}+\frac{3}{8}+\frac{5}{16}+\frac{7}{32}+\dots\]

If the value of the above series can be expressed as \(\frac{a}{b}\) where \(a\) and \(b\) are coprime positive integers. Find \(a-b\).

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