Seems Easy?

Consider the setAA of numbers 1,12,13,.....,12012{1,\frac{1}{2},\frac{1}{3},.....,\frac{1}{2012}} . We delete two of them say aa and bb and in their place we put only one number a+b+aba+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

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