# Using duster over and over and over again!

The numbers $$\space 1 , \frac{1}{2} , \frac{1}{3} , \ldots , \frac{1}{16041998}$$ are written on the black board. Prasun chooses any two numbers say x and y , erases them off using duster and the writes down on the board $$x + y + xy$$ . He continues to do this until the duster dies and only one number is left.

What is this number?

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