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…

Infinite Series

The posts for the next several weeks will be on topics tested only on the BC Calculus exams. The first few weeks will be past posts on sequences and series. That will be followed, in February, by a discussion of Parametric and Vector functions, and Polar equation. We begin with series. Comparison Test Chart A table…

Synthetic Summer Fun

Today, for some summer fun, let’s look at synthetic division a/k/a synthetic substitution. I’ll assume you all know how to do that since it is a pretty common pre-calculus topic and even comes up again in calculus. Why Does Synthetic Division Work? An example: consider the polynomial . This can be written in nested form…