Hi, I'm in precalc and were reviewing trig right now and i'm bored out of my mind. When I was doing a question on my homework I noticed something interesting in one of the questions. I realize that I can prove the answer with trig in about 5 seconds flat but I would like to understand how to use an infinite series sum to describe the relationship first, and then figure out how to find the limit of the series to get my answer as opposed to doing a little trig. Here is a picture of the problem and my thoughts(sorry for the poor quality, all the school has is ms paint :/):

ImageShack - Hosting :: problemdj9.png ImageShack - Hosting :: limitfm0.png
So height z is the sum of the infinite series

First, how would I go about writing the summation to describe the

's?