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Unformatted text preview: 3n feet long and the ant travels 1 foot, so it travels 1/3n ’th of the way down the strip. The first question, whether it ever reaches the end of the strip, is answered by observing that the sum 1/3 + 1/6 + 1/9 + 1/12 + . .. will eventually exceed 1; in fact, the last time it’s less than 1 is at 1/3 + 1/6 + 1/9 + . .. + 1/27 + 1/30 which is about 0.9763. So, after 10 minutes the ant has traveled about 97.63% of the way down the strip, the strip being 33 feet long at that time (after the stretch). When exactly does it get there? It took the ant 10 minutes to travel first 97.63% of the way. The ant had about 33(1 - .9763) feet to go and, since it travels 1 foot per minute, it reaches the end in about another 46.88 seconds. An exact calculation yield a time of 10 minutes 46 37/42 seconds....
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- Spring '10
- Combinatorics, 3 feet, strip, Mike Fitzpatrick, Ray Kremer, Eric Grennan