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S=15+152+253+354+555+856+⋯ 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 S=51+521+532+543+555+568+⋯
If S=ABS = \dfrac ABS=BA, where AAA and BBB are coprime positive integers, find the value of A+BA+BA+B.
Clarification: 1,1,2,3,5,8,…1,1,2,3,5,8,\ldots1,1,2,3,5,8,… follows the Fibonacci Sequence.
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