Thoughts on the power series for , which I found curious. Last week someone asked me a question about the Maclaurin series for . Finding the Maclaurin series is straightforward: Substituting for x gives We can find the radius and interval of convergence by using the Ratio test: This indicates that Maclaurin series…
A know a lot of people like mathematics because there is only one answer, everything is exact. Alas, that’s not really the case. Numbers written as non-terminating decimals are not “exact;” they must be rounded or truncated somewhere. Even things like and 5/17 may look “exact,” but if you ever had to measure something to…
Unit 10 covers sequences and series. These are BC only topics (CED – 2019 p. 177 – 197). These topics account for about 17 – 18% of questions on the BC exam. Topics 10.1 – 10.2 Topic 10.1: Defining Convergent and Divergent Series. Topic 10. 2: Working with Geometric Series. Including the formula for the sum…
This blog post describes a lesson that investigates some ideas about sequences that are not stressed in the AP Calculus curriculum. The lesson could be an introduction to sequences. I think the lesson would work in an Algebra I course and is certainly suitable for a pre-calculus course. The investigation is of irrational numbers and…
The last BC question on the exams usually concerns sequences and series. The question usually asks students to write a Taylor or Maclaurin series and to answer questions about it and its interval of convergence, or about a related series found by differentiating or integrating. The topics may appear in other free-response questions and in…
This is a BC topic Good Question 16 (11-30-2018) What you get when you substitute. Geometric Series – Far Out (2-14-2017) A very interesting and instructive mistake Synthetic Summer Fun (7-10-2017) Finding the Taylor series coefficients without differentiating Error Bounds (2-22-2013) The alternating series error bound, and the Lagrange error bound The Lagrange Highway (5-20-15)…
This is a BC topic POWER SERIES (Maclaurin series and Taylor series) Introducing Power Series 1 (2-8-2013) Making better approximations Introducing Power Series 2 (2-11-2013) Graphing and seeing the interval of convergence Introducing Power Series 3 (2-13-2013) Questions pointing the way to power series Graphing Taylor Polynomials (2-7-2017) Using a graphing calculator to graphs Taylor…
