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N=1+0.02+0.0003+0.000004+⋯+n100n−1+⋯=1.02030405… \large {\begin{aligned} N &=&1 + 0.02 + 0.0003 + 0.000004 + \cdots + \dfrac n{100^{n-1}} + \cdots \\ &=& 1.02030405\ldots\end{aligned}} N==1+0.02+0.0003+0.000004+⋯+100n−1n+⋯1.02030405…
Given that NNN represents an infinite arithmetic-geometric progression sum and it can be expressed as ab\dfrac abba, where aaa and bbb are coprime positive integers. Find a−ba-ba−b.
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