11.2: Series & Convergence (the Calculus Edition)

Action Items:

1. Notes: if you are absent, take notes on the material below as necessary then attempt the homework.

If you are struggling with the topic or need a review of concepts beyond what is contained in my summary notes, refer to Stewart 11.2. We will spend at least three days developing and becoming comfortable with these ideas before moving on.

Key Concepts & Terms:

series
partial sums
convergent series
divergent series
geometric series
the Harmonic Series
Test for Divergence
Sums, differences, and multiples of convergent series

Summary of my 2021 notes with commentary:

Why it matters:

Series can be used to approximate functions by using a partial sum of the series
An infinite series = (partial sum) + (the rest of the terms to infinity); therefore, (infinite series) - (partial sum) = (error)
- we need to know where it is a good approximation of the function: this means we need to know whether and where it converges.
- we need to have a way of measuring how much error is left after we stop adding terms.

2. Practice: None!

Things you MUST KNOW:

What kind of series this is: $LaTeX: a_n=a_1\cdot r^{\left(n-1\right)}$

$LaTeX: S=\frac{a_1}{1-r}$ , when LaTeX: |r|<1

Resources:

Series Homework Solutions

AP Classroom Videos:

10.1: Defining Convergent and Divergent Series
10.2: Working with Geometric Series
10.3: nth Term Test for Divergence