Is It A Converging Series?

Algebra Level 4

S=0.1+0.04+0.009+0.0016+S=0.1+0.04+0.009+0.0016+\cdots SS represents an arithmetic-geometric progression.

If SS can be represented in the form ab\dfrac{a}{b}, where aa and bb are coprime positive integers, find a+ba+b

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