Overview
In Section 8.2, we studied geometric series, in which each of the terms had a special pattern. In the next section, we will extend that idea to series with any kinds of numbers involved. This section has a lot of details involved, so you should focus on understanding the big ideas behind series. In particular, focus on the Basic objectives below to help you organize your studying.
Basic Learning Objectives
These objectives represent the basic calculations, new ideas, etc. in this section. You are responsible for learning and demonstrating that you are proficient with them before class. The preview activity on WeBWorK will cover (some of) these objectives.

Review: Be able to use summation notation proficiently.

State the definition of an infinite series.

Be familiar with the various notations used for infinite series and recognize that they are all equivalent.

State the definition of the \(n\)th partial sum of a series.

State the connection between the sequence of partial sums and the words “convergent” and “divergent”. Explain how all of these are related to the sum of a series.

Be familiar with the statement of the Divergence Test, and why it is useful.
Advanced Learning Objectives
These are the more advanced ideas that we will focus on in class. You should master these objectives during and following class:

Be able to find a formula for the \(n\)th partial sum of a series.

Determine if a series converges or diverges by using the sequence of partial sums.

Be able to use the Divergence Test, Limit Test, and Ratio test proficiently in order to determine if a series converges or diverges. (Note: The textbook also talks about an Integral Test, which you should ignore for now  we will get back to this once we have finished chapter 4.)

Choose the most appropriate convergence test for a given series.
To prepare for class
Use these resources to become proficient with the basic objectives (see above) before class.

Read all of Section 8.3 in the textbook, only ignoring the subsection about the Integral Test (we will come back to this after finishing chapter 5).

Watch the following videos (ignore anything mentioned about the "Integral Test"):

Do the Preview Activity for this section (on WeBWorK if required by your teacher).

Watch the following video:

Do some experimentation with the following interactive applet: Plotting sequences (and also the corresponding partial sums) (melbapplets)
For much later (when we have finished chapter 5 about "Integration")

Watch the following video about the Integral Test: