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.

We still have to work on problems 4 and 5

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.

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

1, 2, 3,

**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

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)