Fibonacci-Geometric Progression!
Calculus
Level
2
\[ \frac{1}{10}+ \frac{1}{10^2}+ \frac{2}{10^3}+ \frac{3}{10^4}+ \frac{5}{10^5}+ \frac{8}{10^6}+ \cdots \]
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 \(A+B\).
by
Manuel Kahayon