week 6

19.2 - Series on positive terms

I think we need to go over more problems here. To feel like we accomplished something in these meetings it would be nice if we ended up being very comfortable determining if series converge or not. Lat week I said to do all odds from this section, if you already did, then do now all evens! I want to discus in detail at least a couple of problems next week.

19.21 Integral test

We still have to work on problems 4 and 5

19.22 Ratio tests

We didn’t talk about many problems here, just #4 o4 # 5 ( I can’t remember). Be sure to have them all. Again, there are very typical questions on this material.

19.31 Absolut and conditional convergence

Kai Be prepared to explain the proof of Theorem IX. Do problems

  • 1, 2, 3,

19.32 Alternating series

Kai be prepared to prove Theorem XII

The observation right before Example 1 is important. It is used to estimate the error when estimating the series. Be sure to understand this.

WOrk problems

  • 1, 2, 3

19.4

Tests for absolute convergence Theorem XIII is known as the ratio test in our textbook. THe nest three theorems are new. Bu sure to understand them and to follow the proofs.

  • 1,

  • 2 a), b), c),

  • 3 )a, b), c),

  • 4 ( just the part about comparing with Gauss’ test)