Sequences and Series Intro
32 min 3 Examples
- Overview of Sequences and Series with terms and definitions
- Writing and simplifying general terms of Sequences
- Simplifying Factorials (3 examples)
- How to determine convergence for an Infinite Sequence
- Overview of the 9 Series test, and the Golden Acronym for determining convergence
Nth Term Test
6 min 3 Examples
- Overview of the Nth Term Test
- 3 Examples
P Series Test
8 min 4 Examples
- Overview of the P Series Test
- 4 Examples
Geometric Series
18 min 4 Examples
- Overview of Geometric Series
- 4 Examples
Limit Comparison Test
23 min 4 Examples
- Overview of Limit Comparison Test
- 4 Examples
Integral Test
19 min 3 Examples
- Overview of Integral Test
- 3 Examples
Telescoping Series
15 min 3 Examples
- Overview of Telescoping Series
- 3 Examples
Alternating Series
20 min 5 Examples
- Overview of Alternating Series Test
- 3 Examples
- Conditional and Absolute Convergence for Alternating Series
- 2 Examples
Ratio Test
22 min 4 Examples
- Overview of Ratio Test
- 4 Examples
Root Test
8 min 3 Examples
- Overview of Root Test
- 3 Examples
Sequences and Series Review
1 hr 6 min 14 Examples
- 12 questions dealing with convergence/divergence for infinite Series
- 2 questions dealing with convergence/divergence for infinite Sequences
Radius and Interval of Convergence
1 hr 4 min 8 Examples
- What is a Power Series? How to find the Radius and Interval of Convergence?
- Example #1: Find the Radius & Interval of Convergence of the Power Series
- Example #2: Find the Radius & Interval of Convergence of the Power Series
- Example #3: Find the Radius & Interval of Convergence of the Power Series
- Example #4: Find the Radius & Interval of Convergence of the Power Series
- Example #5: Find the Radius & Interval of Convergence of the Power Series
- Example #6: Find the Radius & Interval of Convergence of the Power Series
- Multiple Choice – Find the radius of convergence
- Multiple Choice – Find the interval of convergence
Power Series
1 hr 51 min 15 Examples
- Overview of Power Series Representation as Functions
- Examples #1-2: Find the Power Series representation for the function
- Examples #3-4: Find the Power Series representation for the function
- Examples #5-6: Find the Power Series representation for the function
- Example #7: Find the Power Series representation for the function
- Example #8: Find the Power Series representation for the function using Partial Fractions
- Example #9: Find the Power Series representation for the function using Partial Fractions
- Overview of Differentiation Technique to create the sum of a Power Series
- Example #10: Find the Power Series representation for the function using Differentiation
- Example #11: Find the Power Series representation for the function using Differentiation
- Example #12: Find the Power Series representation for the function using Differentiation
- Overview of Integration Technique to create the sum of a Power Series
- Example #13: Find the Power Series representation for the function using Integration
- Example #14: Find the Power Series representation for the function using Integration
- Example #15: Find the Power Series representation for the function using Integration
Maclaurin and Taylor Series Intro
12 min
- Overview of Maclaurin and Taylor Series
Taylor Series
1 hr 38 min 19 Examples
- Overview of the Taylor Polynomial Formula
- 4 Examples for writing a Taylor Polynomial for a given function
- Five Basic Maclaurin/Taylor Expansion Formulas
- Examples using Macluarin Expansions
- More Examples using Maclaurin Expansions
- Power Series and Taylor/Maclaurin Expansion Examples
- 3 Examples using Taylor Expansions to simplify functions and find general terms
- Example of how to evaluate a function using a Taylor Series
- 2 Examples of how to Integrate a function using a Taylor Series
- Example of how to find a value of a Taylor Polynomial
Binomial Series
34 min 3 Examples
- Overview of the Binomial Theorem and the Binomial Series
- Using the Binomial Series instead of the Binomial Theorem
- Example #1: Write the first four terms of the Binomial Series
- Example #2: Write the first four terms of the Binomial Series
- Example #3: Write the first four terms of the Binomial Series
Lagrange Error Bound
1 hr 38 min 12 Examples
- What is True/Actual Error?
- Error for an Alternating Series Overview
- 3 Examples for Alternating Error
- Overview of Taylor’s Remainder Theorem and Lagrange Error Bound
- 5 Examples for finding Lagrange Error
- Overview of Example using all of our Series and Error Techniques
- Part A of Example – Finding a Taylor Polynomial
- Part B of Example – Integrating our Taylor Polynomial
- Part C of Example – Finding the Radius and Interval of Convergence for our Taylor Series
- Part D of Example – Finding Error for our Taylor Polynomial using Alternating Error and Lagrange Error Bound
Chapter Test
3 hr 8 min 39 Examples
- 39 Challenging Practice Problems
- Great for checking your knowledge
- Perfect for preparing for an in-class assessment