Day 32 in MAT229

Today:

• Announcements:
  • 11.2 homework returned. Graded #9, 39.

• Section 11.4: Absolute and Conditional Convergence
  • Assignment: To be handed in (due Thursday, 10/30): pp. 570-571, #7, 10, 11, 14, 17, 20-26, 28

  • Once again, our mission here is not necessarily the value of the series, but may be simply knowledge of whether it converges or not.

    That being said, Theorem 2 below does give us some help in determining the value of (or at least bounds on the value of) the series.

    

    How do they reach the conclusion that the sum is positive and at most a₁?

    

    Let's think of a couple of examples of
    • Series that converge absolutely, and
    • Series that don't.

    

    

    

  • Examples:
    • #2, p. 570
    • #6, p. 570
    • #8, p. 570
    • #18, p. 570:
      

    • #27, p. 570

    • Is conditional convergence the end of commutativity?! Well, sort of!