Class Info

  • Date: Mon Dec 11
  • Meeting Info: 10a-11:40a, N719

Announcements

  • The take-home exercises for Exam #3 were distributed in class, which will be due next Monday (Dec 18)
    • the pdf of the take-home exam exercises are available on OpenLab Files, in case you were absent yesterday or need to print out another copy
    • you can also find the pdf of the “Convergence/Divergence Tests” document I wrote up–that should be helpful for completing the take-home exercises
  • We do not meet tomorrow (Wed Dec 13 – reading day) — I will have office hours during class-time over Blackboard Collaborate instead
  • There will also be a short in-class component for Exam #3 which we will take next Monday Dec 18 (the take-home exercises will serve as preparation for the in-class exam); we will also review for the final exam that day
  • The final exam is in-class on Wednesday Dec 20

Topics

We did a couple more examples of the Ratio Test. We analyzed a series which converges, because the ratio “rho” is turns out to be 1/2 (recall that a series converges by the Ratio Test if rho < 1):

And another series which diverges, because rho turns out to be infinity:

See also #8(c) and (d) from the Final Exam Review for applications of the Ratio Test, including another one involved n! (“n factorial”):

We then discussed alternating series, starting with the definitions of absolute vs conditional convergence. We then went through couple introductory examples, and then discussed the alternating series in #9 from the Final Exam Review.

(Alternating series are discussed in Sec 5.5 of the OpenStax textbook.)

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