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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