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S=0.1+0.02+0.003+0.0004+⋯+n10n+⋯ S = 0.1 + 0.02 + 0.003 + 0.0004 + \cdots + \dfrac n{10^n} + \cdots S=0.1+0.02+0.003+0.0004+⋯+10nn+⋯
Given that the infinite sum S SS can be expressed as ab \frac abba, where aaa and bbb are coprime positive integers, find a+ba+ba+b.
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