# Sum includes powers of 5

Algebra Level pending

Compute :

$\frac{1}{5}+ \frac {1}{5^2} + \frac{2}{5^3}+ \frac{3}{5^4}+ \frac{5}{5^5}+ ... = \frac{A}{B}$

Each numerator is the sum of the two preceding numerators, and each denominator is $$5$$ times the preceding one.

What is $$A+B =?$$ (where $$A$$ and $$B$$ are coprime positive integers).

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