Mysterious Sum

If we have the expression

\[ 1+ 2x + 3x^2 + 4x^3 + 5x^4 + \cdots \] The value of \(1+0.2+0.03+0.004+\cdots \) can be represented as \(\dfrac ab\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).

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