Fibonacci-Geometric Progression!

Calculus Level 2

110+1102+2103+3104+5105+8106+ \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 AB\frac{A}{B}, where AA and BB are coprime positive integers, submit your answer as A+BA+B.

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