Infinite Series & Power Series

Printable version of the Series Mini-Syllabus

Series are "built" from sequences. Sequences can be thought of as functions whose domain is the set of integers. OR sequences are lists of numbers, where the numbers may or may not be determined by a pattern. Bottom line -- series are just a lot of numbers added together. The numbers used come from a sequence. In other words, a series is the sum of a sequence. The main thing we'll deal with for series is to determine whether they converge or diverge. Or, Does this sum equal an actual number or will it add up to "infinity"?

Power Series can be thought of as polynomials that never end -- infinitely many terms. The whole point of this chapter is to rewrite some function as a power series, and then use the power series to make make whatever it was that we wanted to do with the function possible (or at least easier).

Reference

A Chart of Convergence Tests
Visual representations of some types of series
A sum calculator -- for finite & infinite series

Videos/Notes

Topic videos: chapters 5-8
June 7 - notes
June 8 - notes
June 12 - notes
June 13 - notes + 2 extra examples
June 14 - notes
June 15 - notes

Handouts

June 7 - Figure Sequences
June 7 - Sequences: Find the Next Term
June 7 - Sigma: Properties of Summations
June 7 - Geometric and Telescoping Series
June 8 - The Integral and P-Series Tests
June 8 - The Comparison Tests (DCT & LCT)
June 12 - The Alternating Series Test and Absolute Convergence
June 12 - The Ratio Test
June 12 - The Root Test
June 13 - Power Series
June 14 - Using Power Series
June 14 - Building Power Series - the Taylor & Maclaurin Series
June 14 - Building Power Series - the Binomial Series
June 14 - Using Power Series with Integrals
June 15 - Sample Series (key)

Daily Schedule of Topics