1. Sec 11.5: ALTERNATING SERIES
The convergence tests that we have looked at so far apply only to series with positive terms. In this section and the next we learn how to deal with series whose terms are not necessarily positive. Of particular importance are alternating series, whose terms alternate in sign.
An alternating series

2. Sec 11.5: ALTERNATING SERIES
THEOREM: (THE ALTERNATING SERIES TEST)
THEOREM: (THE ALTERNATING SERIES TEST)

3. Sec 11.5: ALTERNATING SERIES
THEOREM: (THE ALTERNATING SERIES TEST)
Example:
Determine whether the series
converges or diverges.

4. Sec 11.5: ALTERNATING SERIES
THEOREM: (THE ALTERNATING SERIES TEST)
Example:
Determine whether the series
converges or diverges.

5. Sec 11.5: ALTERNATING SERIES
THEOREM: (THE ALTERNATING SERIES TEST)
Example:
Determine whether the series
converges or diverges.

6. Sec 11.5: ALTERNATING SERIES
THEOREM: (ALTERNATING SERIES ESTIMATION THEOREM)
Example:
Find the sum of the series correct to three decimal places.

7. Sec 11.5: ALTERNATING SERIES
Example:
Find the sum of the series correct to three decimal places.

8. Sec 11.5: ALTERNATING SERIES
THEOREM: (ALTERNATING SERIES ESTIMATION THEOREM)
REMARK:
The rule that the error is smaller than the first neglected term is, in general, valid only for alternating series that satisfy the conditions of the Alternating Series Estimation Theorem. The rule does not apply to other types of series.

9. Sec 11.5: ALTERNATING SERIES
TERM-102

10. Sec 11.5: ALTERNATING SERIES
TERM-101

11. Sec 11.5: ALTERNATING SERIES
TERM-101

12. Sec 11.5: ALTERNATING SERIES
TERM-092

13. Sec 11.5: ALTERNATING SERIES

14. Sec 11.5: ALTERNATING SERIES

15. Sec 11.5: ALTERNATING SERIES