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?

"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.