Question 9
Let $S$ denote the value of the infinite sum $$
\frac{1}{9} + \frac{1}{99} + \frac{1}{999} + \frac{1}{9999} + \cdots
$$ Find the remainder when the greatest integer less than or equal to $10^{100} S$ is divided by $1000.$
\frac{1}{9} + \frac{1}{99} + \frac{1}{999} + \frac{1}{9999} + \cdots
$$ Find the remainder when the greatest integer less than or equal to $10^{100} S$ is divided by $1000.$