Day 16 in Mat228

Today:

• Announcements
  • Your homework for section 11.3 is due next Thursday.
  • Homework for 11.3 will be pushed back until 10/22.
  • Homework for 11.4 will be pushed back until 10/29.
  • We'll do 11.5 next time (no quiz, as I forgot to make up the worksheet!;)
  • Exam revisions are due today.

• Section 11.4: Absolute and Conditional Convergence
  • 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:
      where is the size of the term (i.e. positive).
      

    • #27, p. 570

    • It turns out that conditionally convergent series can have their terms rearranged to converge to any limit you like. Hmmm.... Is this the end of commutativity?!