We have now developed a tidy model of the cantilevered block problem. We have developed a way of stacking n blocks that can be modeled with a series of increasingly smaller fractions. To determine the distance that a stack of n blocks arranged according to our design can extend beyond the table, we need to find the sum of the first n terms in the series:
To determine the maximum distance that one of our stacks can extend, we need to find the sum of all of the terms in our (infinite) series:
If you have studied infinite series, you might be able to do this directly. But even if you haven't, we have Maple to help us out. You have already seen Maple being used to find the sum of a finite series; it can also find the sum of an infinite series.