Since each succeeding step is exactly 1/2 of the prior step, you have created an infinite geometric series that goes like 4, 2, 1, 1/2, 1/4... The formula for the sum of an infinite geometric series is a/(1-r), where a is the first term and r is the common ratio. Plugging this in, a/(1-r) = 4(1-1/2) = 4/(1/2) = 8. Therefore, you can only travel 8 feet in total and will never! reach the wall.
