UKgrad93 had the general gist of the solution, just didn't do the math correctly as he pointed out. It is a pretty basic calculus concept, that of limits. As numbers are plugged into a function, the sum of all the answers approaches some number - that number is the limit.
For this problem, when dropped the ball falls 2 m. On the first bounce it returns 3/4 of the original height or 1.5 m. Then descends the 1.5 m to the second bounce. It would then reach a height of 1.125 m, etc. Each bounce gets lower and lower until, on the 1,000th bounce or 1,000,0000th bounce, the height it reaches is a small fraction of a meter. Hence, the sum APPROACHES 14 total meters but would never, in theory, actually reach it. In theory, the ball would never stop bouncing even a miniscule fraction of a meter. Hence the concept of limits. The sum will never go above 14 in this example and will only approach 14 no matter how many bounces you want to calculate.
Having taken 4 semesters of calculus and spent almost 10 years as an electrical engineer in a plant, I can tell you I have NEVER used it since college. If I had ever been in design, I most likely would have used it at some point. Now, that I'm in financial planning, I use basic finance and personal finance concepts every day. So, why are engineers made to take so much damn calculus?
