I recorded office hours yesterday morning with a handful of people from class who logged on. We went through a number of examples from the textbook, the WebWork, and the Final Exam Review which are relevant for the take-home exam exercises. You can view the recording on Blackboard (toggle on the menu to “Recordings”):
https://bbhosted.cuny.edu/webapps/collab-ultra/tool/collabultra?course_id=_2317409_1&mode=cpview
I also scanned my notes from the office hours as a pdf and uploaded it to OpenLab Files.
I opened a WebWork set on “Alternating Series”, which consists of a handful of multiple-choice exercises. These exercises should help you think through how to approach alternating series (#6 on the take-home exam). I went through a number of those WebWork exercises during office hours.
Here is a summary of some relevant examples for each of the take-home exam exercises:
#1 (geometric series): See Final Exam Review #8(b). You can also see the examples of this Class Recap (including a screenshot from Sec 5.2 of the textbook, where geometric series are discussed)
#2 (divergence test): We went through examples in Class 25; I went through Example 5.13(a) from the textbook (Sec 5.3) in office hours; see also FER #8(a)
#3 (p-series): Just apply the p-series test, which we discussed in Class 26; see Example 5.15 (also in Sec 5.3)
#4 (limit-comparison test): See the examples in Class 26 and 27, the example in my “Convergence/Divergence Tests” pdf, and the examples from the WebWork “Comparison Tests”
#5 (ratio test): See the examples we did in Class 27 and 28 (which are also written out in the “Convergence/Divergence Tests” pdf), and FER #8(c)(d) — we went through #8(c) in office hours.
#6 (alternating series): See the explanation and examples in Class 28 and the “Convergence/Divergence Tests” pdf, the exercises in FER #9, and the office hours recording.
