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

If you are absent, consult the notes below and check out the appropriate AP Classroom videos. If you are struggling with the topic or need a review of concepts, refer to Stewart 11.6 and the AP videos.

BC 11.6 Summary Notes

BC 11.6 Notes with Examples

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

Homework:

11.6.1: #3-18 all; 19-27 odd. Two-day assignment. This does NOT mean don't do anything one day, and try to cram the others into the second day. It means take your time and do them thoroughly and thoughtfully.

The ratio test, in particular, is used extensively to establish the radius and interval of convergence for power series. It is the basis for earning at least two points in most series FRQs. So yeah, you need to be good at this, too. (The root test doesn't show up as much, if that helps; but Absolute Convergence has been tested recently in FRQs!

Resources:

Series Homework Solutions

AP Videos:

Today's Topics:

10.8: Ratio Test for Convergence

10.9: Determining Absolute or Conditional Convergence

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
10.7: Alternating Series Test
10.10: Alternating Series Error Bound