Look at the following sum 1+1/2+1/4+1/8+1/16+1/32+1/65 notice that the denominator of each fraction in the sum is twice the denominator that comes before it . if you continue adding on fractions according to this pattern, when will you reach a sum of 2?

You will never reach 2, because the value continues to be cut in half. This is often associated with the "half-room" riddle, that says if you walk half way across a room, then one fourth, followed by an eighth, and continue that pattern, will you ever make it to the end of the room? Scientifically you will, but mathematically, you can never.