sc94597 on 02 April 2016
For those saying this really doesn't have a good application/is useless. I found that the concept of a convergent infinite series clicked when this was explained to me when I first learned it in high school, and then again when I learned it in my Calc II class. So at the very least it has a good use to provide intuition when one learns about series, which are very applicable and useful in the application of higher mathematics (I do series expansions quite often in my physics studies.) When I tutor this particular topic I always start with this series, because it really motivates the students I am tutoring.
