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MAT 1236 Calculus III

MAT 1236 Calculus III. Section 11.5 Alternating Series. http://myhome.spu.edu/lauw. HW. WebAssign 11.5 Quiz: 11.3-11.5. Preview. Define Alternating Series Test for Divergence (for Alt. Series) Alternating Series Test (A.S.T.) Alternating Harmonic Series. Definition.

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MAT 1236 Calculus III

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  1. MAT 1236Calculus III Section 11.5 Alternating Series http://myhome.spu.edu/lauw

  2. HW.. • WebAssign 11.5 • Quiz: 11.3-11.5

  3. Preview • Define Alternating Series • Test for Divergence (for Alt. Series) • Alternating Series Test (A.S.T.) • Alternating Harmonic Series

  4. Definition Suppose , the following are the 2 forms of an Alternating Series

  5. Remarks The two forms converge/diverges together. Thus, we are going to use one of two forms for the rest of the discussion.

  6. Notations

  7. (11.2) Test For Divergence If , then is divergent

  8. (11.2) Test For Divergence If , then is divergent

  9. Test For Divergence (Alternating Series Version) For an alternating series, if then so the alt. series diverges

  10. Why?

  11. Why?

  12. Example 1

  13. Alternating Series Test (A.S.T.) If an alternating series satisfies then it converges

  14. Example 2 (Standard Series #4) Alternating Harmonic Series

  15. Example 2 Important details • Identify the series and write down the general terms and • Compare the general terms with range • Take the limit • Make the conclusion by using the A.S.T.

  16. Alternating Series Test (A.S.T.) If an alternating series satisfies then it converges WHY?

  17. Why AST Make Sense? Alternating Harmonic Series

  18. Why AST Make Sense? Alternating Harmonic Series

  19. Why AST Make Sense? Alternating Harmonic Series

  20. Remarks • You can use A.S.T. to show that an alt. series is convergent. • You cannot use A.S.T. to show that an alt. series is divergent. • To show divergence, we need to use Test For Divergence.

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