Serious Series

Algebra Level 4

Let the sum of all terms of the infinite series 2,34,516,964,17256,2,\frac{3}{4},\frac{5}{16},\frac{9}{64},\frac{17}{256},\cdots, be xx.

Let xx have a rational representation as x=abx=\frac{a}{b}, where aa and bb are co-prime.

What is the value of a+ba+b.

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