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 \(a+b\).
by
Arkajyoti Banerjee