Difference between revisions of "AoPS Wiki talk:Problem of the Day/July 28, 2011"
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| + | The distances the ball bounces form a geometric sequence. The sequence goes <math>24, 18, 18, \frac{27}{2}, \frac{27}{2}...</math> infinitely (each, except for the 24, is duplicated because the ball goes up <math>n</math> inches, and comes back down <math>n</math> inches). If we add together the terms that are the same (and add a 24 to the beginning for the sake of a nice pattern), we get <math>48, 36, 27...</math>. | ||
| + | Thus, our solution is <math>\frac{48}{1-\frac{3}{4}}=192-24=\boxed{168 inches}</math>. | ||
Latest revision as of 10:04, 28 July 2011
Problem
AoPSWiki:Problem of the Day/July 28, 2011
Solution
The distances the ball bounces form a geometric sequence. The sequence goes 
infinitely (each, except for the 24, is duplicated because the ball goes up 
inches, and comes back down inches). If we add together the terms that are the same (and add a 24 to the beginning for the sake of a nice pattern), we get 
.
Thus, our solution is 
.
