# Unit 10 – Infinite Sequences and Series

Introductory Ideas suitable for calculus classes and classes before calculus Taylor Polynomials for ln(x) centered at x = 1N = 1, 2, 3, 4, 5 and 6

Amortization – An important real-life use of Geometric Series – no calculus involved.

The Hindu-Arabic Series – the most import series.

Everyday Series – Numbers are series.

A Lesson on Sequences – All real numbers are sequences.

Convergence Tests

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.

Power Series

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 $displaystyle cos left( {sqrt{x}} right)$

Error Bounds

What’s the “Best” Error Bound?  – On error bounds.

The Lagrange Highway – a way of explaining the Lagrange error bound.