Seems Easy?

Number Theory Level 4

Consider the set\(A\) of numbers \({1,\frac{1}{2},\frac{1}{3},.....,\frac{1}{2012}}\) . We delete two of them say \(a\) and \(b\) and in their place we put only one number \(a+b+ab\). After performing the operation 2011 times what is the number that is left over.

Note- It's an old NMTC Junior level problem