ADVANCE CALCULUS: ALTERNATING SERIES.pptx

ADVANCE CALCULUS: ALTERNATING SERIES

1. Alternating series Alternating series Lesson 21 Kyla Dianne garibay

2. TOPICS Alternating Series Test Conditional and Absolute Converges Approximations

3. Alternating Series Let , then  

4. Alternating Series Test Given an alternating series   Where , converge if: , for all  

5. Example   1. Identify     2.       3.         Converges

6. Example   1. Identify     2.       3.         Converges

7. Example      

8. Example   1. Identify     2.       3.         Conditionally Converges    

9. Conditionally Convergent Series is conditionally convergent if converges but diverges  

10. Example   1. Identify     2.       3.         Converges

11. Example   Converges   Converges ABSOLUTELY CONVERGENT  

12. Example   1. Identify     2.       3.         Converges

13. Example   Diverges   p - series Converges CONDITIONALLY CONVERGENT

14. Example   1. Identify     2.       3.         Converges

15. Example   1. Identify     2.       3.         Converges

16. Example Diverges harmonic series Converges CONDITIONALLY CONVERGENT    

17. Example Converges p - series Converges ABSOLUTELY CONVERGENT    

18. Example Diverges      

19. Approximation Given a convergent alternating series, is the sum of the series, is the nth partial sum, Then   Error in approximating the entire sum with the  

20. Theorem If a convergent alternating series satisfies the condition , then the absolute value of the remainder  

22. Thank you Thank you