2014 AMC 12A Problems/Problem 23
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Problem
The fraction ![\[\dfrac1{99^2}=0.\overline{b_{n-1}b_{n-2}\ldots b_2b_1b_0},\]](http://latex.artofproblemsolving.com/2/e/1/2e1249826c419acf9b5a00eb3f3f9acb191cc1d1.png)
where 
is the length of the period of the repeating decimal expansion. What is the sum 
?
