# Question #a6740

##### 1 Answer
Jun 9, 2017

As indicated in the comments the racer's flags will be alternating so fast their combination will look purple. The racer's finite size will prevent him from attaining a true finish.

#### Explanation:

If the racer can reach only half the distance to his goal on each try, he will conceptually never achieve it.

But the reciprocals of powers of $2 ,$ which are $\frac{1}{2} , \frac{1}{4} , \frac{1}{8} , \frac{1}{16} , \ldots$ will eventually result in a convergent series. So if the flag changing could be kept up indefinitely, the racer would reach a finish.

https://en.wikipedia.org/wiki/Convergent_series

The racer will arrive at a physical end position at some point in time, but due to his physical size, he will still be half way from his destination no mater how small that distance is, so he cannot complete the mission.