# Too many 5s

Algebra Level 4

If the sum $$\large \displaystyle \sum_{n=1}^{\infty} \dfrac{\overbrace{5555 \ldots 5}^{\text{n times}}}{13^n}$$ can be represented as $$\dfrac{A}{B}$$ where $$A$$ and $$B$$ are coprime positive integers, find $$A+B$$.

Clarifications

The expanded form of above sum is $$\dfrac{5}{13} + \dfrac{55}{13^2} + \dfrac{555}{13^3} + \ldots$$

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