11.9: Representations of Functions as Power Series

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

11.9 Notes.

Why should we care:

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

Homework: 11.9.1: #3-10; 13-17 odd, 16 & 23. Two day assignment (plus the break). DO NOT leave them until Sunday evening February 25th! 🙄

Resources & Stuff you must know:

All the convergence tests & geometric series rules! Summary of Convergence Tests

Memorize the 5 Common Power Series ! (Note, I don't need you to have the ln series memorized). I will start quizzing on these after mid-winter break.

Series Homework Solutions

AP Videos!!!

10.1: Defining Convergent and Divergent Series
10.2: Working with Geometric Series
10.3: nth Term Test for Divergence
10.4: Integral Test for Convergence (2 videos)
10.5: Harmonic Series and p-series (1 video)
10.6: Comparison Tests for Convergence
10.7: Alternating Series Test
10.8: Ratio Test for Convergence
10.9: Determining Absolute or Conditional Convergence
10.10: Alternating Series Error Bound
10.13: Radius & Interval of Convergence for a Power Series
10.15: Representing Functions as Power Series