CONO-SUR 1992 Problem 3

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?