11.7 Summary of Convergence Testing

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

No new notes! We've learned all the convergences tests you are responsible for knowing. Time to spend some time synthesizing and revising your knowledge and understanding. 🤓

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!

The one page Summary of Convergence Tests

Homework: None! Save this for tomorrow. 🤓

LP WS: Tools for Testing Convergence of a Power Series

Resources:

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