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If the sum ∑n=1∞5555…5⏞n times13n\large \displaystyle \sum_{n=1}^{\infty} \dfrac{\overbrace{5555 \ldots 5}^{\text{n times}}}{13^n}n=1∑∞13n5555…5n times can be represented as AB\dfrac{A}{B}BA where AAA and BBB are coprime positive integers, find A+BA+BA+B.
Clarifications
The expanded form of above sum is 513+55132+555133+…\dfrac{5}{13} + \dfrac{55}{13^2} + \dfrac{555}{13^3} + \ldots135+13255+133555+…
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