Fibonacci-Geometric Progression!

Calculus Level 3

\[ \frac{1}{10}+ \frac{1}{10^2}+ \frac{2}{10^3}+ \frac{3}{10^4}+ \frac{5}{10^5}+ \frac{8}{10^6}+ \cdots \]

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

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

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