# Gauss Returns!

Algebra Level 2

$S = 0.1 + 0.02 + 0.003 + 0.0004 + \cdots + \dfrac n{10^n} + \cdots$

Given that the infinite sum $$S$$ can be expressed as $$\frac ab$$, where $$a$$ and $$b$$ are coprime positive integers, find $$a+b$$.

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