Undoubtedly Rational

Algebra Level 4

N=1+0.02+0.0003+0.000004++n100n1+=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}}

Given that NN represents an infinite arithmetic-geometric progression sum and it can be expressed as ab\dfrac ab, where aa and bb are coprime positive integers. Find aba-b.

×

Problem Loading...

Note Loading...

Set Loading...