# Undoubtedly Rational

Algebra Level 4

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

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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