Too many 5s

Algebra Level 4

If the sum n=155555n times13n\large \displaystyle \sum_{n=1}^{\infty} \dfrac{\overbrace{5555 \ldots 5}^{\text{n times}}}{13^n} can be represented as AB\dfrac{A}{B} where AA and BB are coprime positive integers, find A+BA+B.

Clarifications

The expanded form of above sum is 513+55132+555133+\dfrac{5}{13} + \dfrac{55}{13^2} + \dfrac{555}{13^3} + \ldots

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