An athlete is able to jump FOREVER. However, every time that she jumps she gets a bit more tired, and every jump goes 1/2 as far as her prior jump. Now, for her very first jump, she goes 1/2 of a foot. On her second jump, she goes 1/4 of a foot, and so on and so forth.
The athlete will never reach one foot because they only ever jump half of the remaining distance