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July 24, 2014

July 24, 2014

Posted by **Tia** on Monday, December 5, 2011 at 7:24pm.

- math -
**Reiny**, Monday, December 5, 2011 at 10:05pmIn 10 moves, Rodney has covered 10 feet , so he is 20 ft from the door

in 10 moves , James has moved:

15 + 15/2 + 15/4 + 15/8 + 15/16 + .. + 15/2^9

this is a geometric series with a= 15, r = 1/2

sum(10) = 15(1 - (1/2)^10)/(1 - 1/2)

= (1023/1024)(30)

so he is (1/1024)(30) feet away from the door

notice on the 10th move, he is 1/2^10 of the distance away.

moving in this fashion , James will never get to the door

e.g., after 1000 moves he would still be (1/2^1000) of the distance away from the door

whereas Rodney will clearly reach the door after 30 moves.

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