1. 1 Lecture 28 – Alternating Series Test Goal: Does a series (of terms that alternate between positive and negative) converge or diverge?

2. 2 Alternating Series Test A series of the form with is called alternating and converges if:

3. Example 1 – Converge/Diverge? 3

4. Example 2 – Converge/Diverge? 4

5. Example 3 – Converge/Diverge? 5

6. Example 4 – Converge/Diverge? 6

7. Using S n (nth partial sum) to approximate S 7 The remainder term when using S n :

8. Example 5 8 How many terms are needed to approximate the series and yield a remainder less than 0.0001?

9. Absolutely Converge, Conditionally Converge, or Diverge 9

10. Example 6 – AC, CC, D? 10 Look at absolute value:

11. Example 7 – AC, CC, D? 11 Look at absolute value:

12. Example 8 – AC, CC, D? 12 Look at absolute value: