1. Section 8: Alternating Series

2. A series in which the terms alternate sign.
Alternating Series:
A series in which the terms alternate sign.

3. The Alternating Series Test
Series converges if:
Alternates
Terms decrease in magnitude
Terms approach zero

4. Ex 1: converge or diverge? A) B)

5. Ex 1: converge or diverge? C) D)

6. Alternating Series Error Bound:

7. Ex 2: Use S5 to give bounds for the value of:

8. Ex 3: Using the alternating series bound, what degree Maclaurin polynomial is required to estimate cos(3) with an error of no more than 0.001?

9. If converges, then is Absolutely Convergent.
If diverges and
converges, then is Conditionally Convergent.

10. Ex 4: Absolutely Convergent, Conditionally Convergent or Divergent. A)
Ex 4: Absolutely Convergent, Conditionally Convergent or Divergent? A) B)

11. Ex 4: Absolutely Convergent, Conditionally Convergent or Divergent? C)

12. Ex 5: Find the Interval of convergence:

13. Section 8 WS