A rubber band is 1 meter long. An ant starts at one end, crawling at 1 millimeter per second. At the end of each second, the rubber band is instantaneously stretched by an additional meter. (So, at the end of the nth second, the rubber band becomes n+1 meters long.)

Does the ant ever reach the far end of the band? If so, when?

n=time in seconds
m=millimeters the ant has travelled
n=m
1000+n1000=length of the rubber band
the ant has travelled the length of the rubber band when:
n=1000+n1000
n-n1000=1000
-999n=1000
means the solution for n is not positive
means the ant walks forever

Posted by James D Brown on 2002-10-03 16:42:01