Being a big fan of duct Jason has twelve brand new rolls out in the garage, but unfortunately none of them say how much tape is on a roll! To help Jason plan out a big duct tape project can you figure out how much tape is contained on each roll? You are able to measure that the tape is wrapped around a cardboard tube with an outer diameter of two inches, and that the tape wraps around the tube until it has an outer diameter of 3.5 inches. The tape measures out to be 0.01 inches thick. What length of tape is contained on each roll?
The wording needs a bit of work – specifically I want to add some reason why Jason wants to know how much tape is on each roll – but for now I am stumped. I originally wrote it with him wanting to make a suit out of duct tape for his high school reunion – but the absurdity eclipsed the problem. Eclipsing the problem is sort of an ongoing problem when I write this stuff up.
My main problem here, I think, is that it is a very simple problem if you have the tools to solve it – but I am not sure if it is too difficult if people have never worked with power series. I wrote up the solution as an introduction to them – and that is the goal of this problem: to get people thinking with power series.
As always my answer is on the book site I set up. The comments below are just for discussing the problem / people to post their answers.