Class Info

  • Date: Mon Dec 4
  • Meeting Info: 10a-11:40a, N719

Announcements

WebWork:

  • “Series – Divergence Test” – due Wed Dec 6
  • “Series – Comparison Tests” – due Wed Dec 13

Schedule for the rest of the semester:

I outlined the schedule for the rest of the semester:

  • We have class tomorrow (Wed Dec 6) and Monday Dec 11, where we will cover additional topics on infinite series–please work on the WebWork sets on this material!
  • Exam #3 will consist of a take-home component which will be distributed in class next 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 which we will take that Monday Dec 18 (the take-home exericses 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
  • See the 1st board snapshot below for a day-by-day outline of the schedule

Topics

See the schedule on the left-hand side:

We briefly discussed the integral test, as a way of classifying “p-series”:

The integral test and p-series test are covered in Sec 5.3.

We then introduced the limit-comparison test, which is used to “compare” a given infinite series to one we know converges or diverges; the test consists of looking at the limit as n goes to infinity of the ratio a_n / b_n.

In this first example, we compared the given series (Sigma 1/(n^2+1) to the p-series with p=2, since they are very similar, and we know the latter converges:

Here is the presentation in the textbook (from Sec 5.4), which starts with a similar example:

We then outlined two examples from the textbook:

We will do a couple more examples of the limit-comparison test tomorrow from the WebWork, then go on to discuss alternating series.