# Fibonacci on fives

Calculus Level 3

$S =\frac{1}{5} + \frac{1}{5^{2}} + \frac{2}{5^{3}} + \frac{3}{5^{4}} + \frac{5}{5^{5}} + \frac{8}{5^{6}} + \cdots$

If $$S = \dfrac AB$$, where $$A$$ and $$B$$ are coprime positive integers, find the value of $$A+B$$.

Clarification: $$1,1,2,3,5,8,\ldots$$ follows the Fibonacci Sequence.

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