# 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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