Drib problem

A Zeno's Paradox Problem

The following problem is a version of Zeno's paradox. It is taken from an article by George Andrews in the January 1998 issue of the American Mathematical Monthly, Vol. 105 No. 1 and is attributed to a Prof. Sleator.

Two trees are one mile apart. A drib flies from one tree to the other and back, making the first trip at 10 miles per hour, the return at 20 miles per hour, the next at 40 and so on, each successive mile at twice the speed of the preceeding. When will the drib be in both trees at the same time? Hint: Write an expression for the time it takes to travel n miles. What happens as n goes to infinity?