Good Question 16

I had an email last week from a teacher asking, how come I can use a substitution to find a power series for  , and for  , but not for  ? The answer is that you can. Substituting (2x) in to the cosine’s series give you a Taylor series centered at x = 0, a…

Good Question 14

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…

Which Convergence Test Should I Use? Part 1

One common question from students first learning about series is how to know which convergence test to use with a given series.  The first answer is: practice, practice, practice. The second answer is that there is often more than one convergence test that can be used with a given series. I will illustrate this point…

More on Power Series

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?…

Introducing Power Series

The posts for the next several weeks will be on topics tested only on the BC Calculus exams. Continuing with some posts on introducing power series (the Taylor and Maclaurin series) Introducing Power Series 1 Two examples to lead off with. Introducing Power Series 2 Looking at the graph of a power series foreshadows the…