# Using duster over and over and over again!

**Discrete Mathematics**Level 4

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?