Fibonacci-Geometric Progression!

Calculus Level 3

$\large {\frac{1}{10} +\frac{1}{10^2}+ \frac{2}{10^3}+ \frac{3}{10^4}+\frac{5}{10^5}+\frac{8}{10^6}+ \cdots}$

Find the sum of the above sequence, where the denominators follow a geometric progression, and the numerators follows the Fibonacci sequence.

If you get your answer as $$\dfrac{A}{B}$$, where $$A$$ and $$B$$ are coprime positive integers, submit your answer $$A+B$$.

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