What's the Final Number ?

Consider the set

S={1,12,13,14,,1100}. S= \left \{ 1, \frac {1}{2}, \frac {1}{3}, \frac {1}{4},\cdots, \frac {1}{100} \right \}.

Choose any two numbers xx and y,y, and replace them with x+y+xy. x+y+ xy.

For example, if we choose the numbers 12\frac{1}{2} and 18\frac {1}{8}, we will replace them by 1116 \frac {11}{16} .

If we keep repeating this process until only 11 number remains, what is the final number?


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