Undoubtedly Rational

Algebra Level 4

\[ \large {\begin{eqnarray} N &=&1 + 0.02 + 0.0003 + 0.000004 + \cdots + \dfrac n{100^{n-1}} + \cdots \\ &=& 1.02030405\ldots\end{eqnarray}} \]

Given that \(N\) represents an infinite arithmetic-geometric progression sum and it can be expressed as \(\dfrac ab\), where \(a\) and \(b\) are coprime positive integers. Find \(a-b\).

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