Question 304621: Suppose an indecisive man starts out from home and walks 1 mi east,then 1/2 mi west, then 1/4 mi east, then 1/8 mi west, and so on. Relative to his home, approximately where would he end up?
I have no clue..please help.
Thanks
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Suppose an indecisive man starts out from home and walks 1 mi east,then 1/2 mi west, then 1/4 mi east, then 1/8 mi west, and so on. Relative to his home, approximately where would he end up?
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Total lateral distance: 1-(1/2)+(1/4)-(1/8)+(1/16)-(1/32)....
= [1 + 1/4 + 1/16 + 1/64... ] - [1/2 + 1/8 + 1/32]
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Using the sum of a geometric series you get:
= (1)[1/(1-(1/4)] - (1/2)[1-(1/4)]
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= 1/(3/4) - (1/2)/(3/4)
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= 4/3 - 2/3
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= 2/3
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Cheers,
Stan H.
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