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S=0.1+0.04+0.009+0.0016+⋯S=0.1+0.04+0.009+0.0016+\cdotsS=0.1+0.04+0.009+0.0016+⋯ SSS represents an arithmetic-geometric progression.
If SSS can be represented in the form ab\dfrac{a}{b}ba, where aaa and bbb are coprime positive integers, find a+ba+ba+b
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