MathDB

The number

1

is written on the blackboard. At any point, Kornny may pick two (not necessary distinct) of the numbers

a

and

b

written on the board and write either

ab

\frac{1}{a}+\frac{1}{b}+\frac{1}{ab}

on the board as well. Determine all possible numbers that Kornny can write on the board in finitely many steps.

9