Question 23
The fraction $$
\dfrac{1}{99^2}=0.\overline{b_{n-1}b_{n-2}\ldots b_2b_1b_0},
$$ where $n$ is the length of the period of the repeating decimal expansion. What is the sum $b_0+b_1+\cdots+b_{n-1}?$
\dfrac{1}{99^2}=0.\overline{b_{n-1}b_{n-2}\ldots b_2b_1b_0},
$$ where $n$ is the length of the period of the repeating decimal expansion. What is the sum $b_0+b_1+\cdots+b_{n-1}?$