You will laugh at this. There was this popular math problem that goes like this: Two trains are approaching each other at some speed. A bird flies back and forth between the trains. How many trips will the bird make before the trains collide?
Apparently the answer is Infinite using some concept similar to what you mentioned. The gap between the trains keeps reducing as a fraction of the original gap between them, and this goes on reducing to an infinitely small number without actually becoming zero. I don't know how this is possible practically speaking. But such is the weirdness of math
Some one talks about that problem here:
http://www.physicsforums.com/archive/index.php/t-130033.html
http://www.physicsforums.com/archive/index.php/t-156582.html