Class Info

  • Date: Wed Dec 6
  • Meeting Info: 10a-11:40a, N719

Announcements

WebWork:

  • “Series – Comparison Tests” – due Wed Dec 13

Reminder – schedule for the rest of the semester:

  • Exam #3 will consist of a take-home component which will be distributed in class Monday (Dec 11) and will due the following Monday (Dec 18)
  • We do not meet on Wed Dec 13 (Tues Dec 12 and Wed Dec 13 are reading days, so no classes will meet)
  • There will also be an in-class component for Exam #3 which we will take that 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 some more examples of the limit-comparison test, illustrating the strategy of looking at the degrees of the numerator and denominator in order to identify a p-series to compare the given series to (in the case when the given series is a rational function of n, i.e., a ratio of two polynomials); use this strategy for the “Series – Comparison Tests” WebWork exercises.

We also introduced the Ratio Test–this is a way of identifying series that are “almost geometric” as n gets large, and using that to classify them as convergent or divergent:

The conclusion for the example above is that the given series converges, since it’s value of “rho” = 1/2, which is less than 1 (see my “Convergence/Divergence Tests” pdf for this example typed up there).

The Ratio Test is covered at the start of Sec 5.6:

We will use the ratio test to study “power series” which will be the last topic we cover, on Monday (see Sec 6.1).

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