Smart Grandsons

Mothers day dinner was fun. For some reason Sam was fixated on a question. If you always move halfway to a destination do you ever get there. After some discussion he started with the idea that if you were half way there the next time you would be a fourth. Then 1/8, 1/16, 1/32, 1/64, 1/128, 1/256 and on to 1/512, 1/1024. Then would that be apart or a hair apart. Meanwhile I was impressed with his understanding of the concept that he developed on his own. Also how quickly he did the math in his head for a 3rd grade kid. Second grade Miles also did the math. Of course even that did not answer the question. What do you think? If you always went halfway to your destination would you ever get there?