This problem can be simplified.
Imagine, you want to get to the number 2. You start by adding the half of 2, 1. 0+1=1, *dUh*. Then, you add half of 1, 0.5. You get 1.5. Next, you get 1.75, 1.875, etc, etc. If you go on infinitely, you will eventually get to 2.