Introductory Ideas suitable for calculus classes and classes before calculus
Amortization – An important real-life use of Geometric Series – no calculus involved.
Everyday Series – Numbers are series.
A Lesson on Sequences – All real numbers are sequences.
Which Convergence Test Should I Use? Reference Chart. A PDF summarizing the convergence tests.
Which Convergence Test Should I Use? Part 1 – On series, many possible tests.
Which Convergence Test Should I Use? Part 2 – How to decide on which convergence test to try.
Good Question 14 – On the integral test.
Introducing Power Series 1 – Two preliminary examples.
Introducing Power Series 2 – Graphing the examples from above and identifying further explorations.
Introducing Power Series 3 – Looking forward.
Graphing Taylor Polynomials – (8) How to use a grapher to see a series and its interval of convergence.
New Series from Old 1 – By substitution.
New Series from Old 2 – By differentiating and integrating.
New Series from Old 3 – Rational Functions and a great “mistake.”
Geometric Series – Far Out – A very instructive mistake.
Synthetic Summer Fun – Synthetic division: how it works, why it works, and using it for Taylor Series
Good Question 16 – 2004 BC 6(a) Trig formulas to the rescue.
A Curiosity – On the series for
What’s the “Best” Error Bound? – On error bounds.
The Lagrange Highway – a way of explaining the Lagrange error bound.