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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 101+1021+1032+1043+1055+1068+⋯
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}BA, where AAA and BBB are coprime positive integers, submit your answer as A+BA+BA+B.
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