Day 31 in MAT229

Last time

Next time

Announcements:
- We're in week 9, and today we start sequences and series.
- Note that we have a "spring break" day this week, so I'm going to issue two days of new notes only -- nothing on Friday. So tomorrow you'll have a lab, and more new material on Wednesday only.
  Friday you should relax and have some fun.
- I've graded everything up to the lab you turned in on Saturday (IMath portion of the exam, which saw some dramatic changes to some of you; Weekly 5 assignment (still have a few of these to grade -- key .nb, and .pdf); Lab 7 (key .nb, and pdf)).
  It definitely would have been helpful had you had the feedback from weekly assignment 5 and Lab 7 for the exam. That's my bad, so I'm going to only count exam 2 in your final grade if it benefits you.
  I may use your performance on it, however, to give some impression of how you are doing at midterm (those grades are due next week).
- I'm pushing back your homework due date on weekly homework 6 to Wednesday, because I can't get to it before then anyway....
Today:
1. We're switching gears once again. But let me give you some context for the switch. We're going to start by talking about sequences. These are infinite, ordered lists of numbers: e.g., the natural numbers $\{1,2,3,\ldots\}$.
  More generally $\{a_1,a_2,a_3,\ldots\}$.
2. Because these sequences are running off to infinity, we wonder how they behave way out there. So the issues of convergence and divergence occur in this context as well (just like in improper integrals).
3. In today's "lecture", I cover the Mathematica notebook, beginning with a little review of comparison for improper integrals; then on to some examples of sequences you've already encountered, and some that are several thousand years old!
Materials for today:
Links/Notes:
- Nothing new to report.

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