There are 2 boys standing on a road, one kilometer apart from eachother. The boys names are Pete and John. Pete starts to run after John, moving at 1 meter per second. After 1 second the road stretches uniformly and instantaneously by 1 kilometer so now John is 1998 meters away from Pete. Pete tries to speed up but is still moving at 1 meter per second. After another second the road stretches again by 1 kilometer so now Pete is 2995.5 meters away. This keeps happening over and over again.
Does Pete ever catch up to John?
If he does, how long does it take?
set up a sequence where Dn represents the distance between Pete and John after n seconds, but before the road does its instantaneous stretch(immediately after the step but before the stretch)
find a general expression for Dn in terms of D0
At second n the road scales by a factor (n+1)/n, If just at n-1 the distance
between the boys is D(t-1), then: