Here is my annual pitch for my series chapter. Version 1.3, new for the 2012-2013 school year, has been posted to the designated deriver wiki. (Click here: http://designatedderiver.wikispaces.com/BC+topics -- the chapter is about half way down and is titled "Series Chapter v1.3.) For those familiar with the chapter, not much is changed in the latest version. There are a couple more problems on telescoping series, by request, but mostly this revision was just about another layer of polish and some error correction, both in the text and in the solutions.
For those new to the listserv, my chapter is a complete, stand-alone chapter on the series topics for BC Calculus. It is organized differently from how the material is treated in most textbooks. It starts with a discussion of Taylor polynomials and then moves on to power series and ultimately Taylor series. Convergence tests come in when they are needed -- to figure out intervals of convergence of power series. The idea is that by starting with the more concrete ideas of Taylor polynomials, students will be in a better place to appreciate what is happening when we extend to infintely many terms in a Taylor series. This approach has been advocated many times in this forum, and the feedback I have received on the chapter has been positive. If you would like to know more about the chapter and the thinking behind it, I encourage you to download it and read the preface. You are free to use the chapter however makes sense to you. You can email the entire document to students, post it on your course web pages, whatever suits you. (I don't recommend printing it out for each kid, both because that's a lot of paper and because I wouldn't want to lose the color in the graphs.) I only ask that if you use the chapter, please send me feedback (corrections, comments on areas that need clarification, thoughts on how useful the text is, etc.). Since this is a personal project, not a work project, please send emails to me at: bunderscoregoldstein at yahoo dot com.