Serious Series

Algebra Level 4

Let the sum of all terms of the infinite series \(2,\frac{3}{4},\frac{5}{16},\frac{9}{64},\frac{17}{256},\cdots\), be \(x\).

Let \(x\) have a rational representation as \(x=\frac{a}{b}\), where \(a\) and \(b\) are co-prime.

What is the value of \(a+b\).

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