Consider the set $S$ of $100$ numbers: $1; \frac{1}{2}; \frac{1}{3}; ... ; \frac{1}{100}$. Any two numbers, $a$ and $b$, are eliminated in $S$, and the number $a+b+ab$ is added. Now, there are $99$ numbers on $S$. After doing this operation $99$ times, there's only $1$ number on $S$. What values can this number take?