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20 February, 04:39

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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  1. 20 February, 04:53
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    "and so on" leads me to believe that this is an infinite geometric sequence which will always have a sum (if r^2<1) of:

    s=a / (1-r) where s=sum, a=initial term, and r is the common ratio ...

    If we designate east as positive and west as negative the sequence is:

    1,-1/2,1/4,-1/8 so the common ratio is - 1/2 and a=1 thus:

    s=1 / (1--1/2)

    s=1 / (3/2)

    s=1 (2/3)

    s=2/3 of a mile east of his home.
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