I am standing 10 feet from a wall. I will begin to walk toward the wall and my first step is 4 feet. Each succeeding step is exactly one half the distance of the prior step. So my next step would be 2 feet, then 1 foot etc. How many steps will it take me to reach the wall?

Never!

Step-by-step explanation:

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.