# 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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