11.8 Power Series

If you are absent, check out the appropriate AP Classroom videos.

Notes: A power series is literally a polynomial series built with powers of x (hence "power" series). Notice, too, that if you are multiplying by "x" for each term, they are also Geometric series. If you were absent or just want a review of what we went over today: Notes on Power Series.

Why convergence matters:

Series can be used to approximate functions by using a partial sum of the series
An infinite series = partial sum + the rest of the terms; therefore, (series) - (partial sum) = error
- we need to know where it is a good approximation of the function: whether and where it converges.
- we need to have a way of measuring how much error is left after we stop adding terms

Stuff you must know: all the convergence tests & geometric series rules!

Start Memorizing the 5 Common Power Series!

Summary of Convergence Tests

Homework: 11.8 #1-10; 11-15 odd; 16 - 25 all. (Two day assignment).

Resources:

Series Homework Solutions

AP Videos!!!

10.13: Radius and Interval of Convergence of a Power Series