Fibonacci-Geometric Progression!

Calculus

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

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

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