# Fibonacci Fractions

$0.1+ 0.01+ 0.002+ 0.0003+ 0.00005+ 0.000008+\ldots$

The series above shows the sum of all $$n^\text{th}$$ Fibonacci number, shifted $$n$$ places to the right (that is, divided by $$10^n$$). If its closed form can be represented as $$\frac a b$$ for coprime positive integers, find $$a+b$$.

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