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. SEQUENCES Everyday series (1-17-2017) The most familiar series: Numbers Amortization (2-9-2015) An important use of a (finite) series – Find you mortgage payment without calculus. Convergence Test List A summary of the tests. Download and copy for your students (and yourself) Which Convergence Test Should I Use? Part 1 (2-9-2018)…
Good Question 14 – The Integral Test I have no criteria for what constitutes a “Good Question” for this series of occasional posts. They are just questions that I found interesting, or that seem more than usually instructive, or that I learn something from. I cannot quote this question (2016 BC 92) since it is…
Continuing with post on sequences and series New Series from Old 1 Rewriting using substitution New Series from Old 2 Finding series by differentiating and integrating New Series from Old 3 Rewriting rational expressions as geometric series Geometric Series – Far Out A look at doing a question the right way and the “wrong” way?…
Convergence tests for series appear on both sections of the BC Calculus exam. In the multiple-choice section, students may be asked to say if a sequence or series converges or which of several series converge. The Ratio test is used most often to determine the radius of convergence and the other tests to determine the…
