I'm assuming the first step is supposed to be half the distance, so that, with an infinite number of steps, you cover 99.999999999...% of the distance.

There's an old joke about a mathematician and an engineer arguing about this problem. The set-up is that they must cross from one end of the room to the other, where there is (ahem) a beautiful woman. The mathematician doesn't bother even trying, because he calculates that you could never make it all the way across. The engineer grins and avidly pursues his infinite step journey across the room. The mathematician scoffs at him. "You'll never make it!" The engineer says, "Who cares? I'll get close enough for all practical purposes!"

Seriously, there's a case to be made that you WILL reach your target. See Brain Food's mathematical reasoning puzzles, #12.