11.5.2: Alternating Series Test & Error

1. Alternating Series Error Bound Notes: BC 11.5: AST Error Bound Notes. AST is used often, and the AS Error Bound is one of only two approximations for error tested on the exam. Be sure you do everything you can to be comfortable with these!

2. If you did not finish HW: 11.5.2: #7-19 all; PLUS #21-29; do so!

11.6: Absolute Convergence, and the Ratio and Root Tests for Convergence

3. [Begin] Absolute Convergence, and the Ratio and Root Tests for Convergence Notes:

BC 11.6 Summary Notes

BC 11.6 Notes with Examples

4. Begin HW: 11.6: #3 - 18 all; 19 - 27 odd. (You will have until Wednesday for these.)

Why Convergence & Error matter:

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

Things you MUST KNOW:

Divergence Test

Integral Test

Direct Comparison Test

Limit Comparison Test

P-series Test

Harmonic Series

What kind of series this is:

$LaTeX: a_n=a_1\cdot r^{\left(n-1\right)}$

and what this is: $LaTeX: S=\frac{a_1}{1-r}$ , when LaTeX: |r|<1

Resources:

Series Homework Solutions

AP Classroom Videos:

10.7: Alternating Series Test

10.10: Alternating Series Error Bound

Or catch up with one of the previous AP videos (I highly recommend these, whether you think you fully understand everything or not!)!

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 (2 videos)