Sequences
1 hr 21 min 23 Examples
- Introduction to Video: Introduction to Sequences
- Overview of Sequences
- Definitions: Finite, Infinite, Convergent, Divergent, Recursive and Monotonic
- Examples #1-4: Find the Explicit Formula (rule) for each Sequence
- Examples #5-9: Write the first five terms of the sequence
- Examples #10-15: Simplify the Factorial Expression
- Examples #16-17: Write the first four terms of the sequence
- Examples #18-19: Graph the Sequence
- Examples #20-23: Determine if the Sequence is Monotonic
Geometric Sequences
1 hr 10 min 19 Examples
- Introduction to Video: Arithmetic and Geometric Sequences
- Overview of Recursive, Arithmetic and Geometric Sequences and Formulas
- Examples #1-4: Write the first five terms of the Arithmetic or Geometric Sequence
- Examples #5-6: Find the indicated term and the general term of the Arithmetic Sequence
- Example #7: Find the indicated term and the general term of the Arithmetic Sequence
- Examples #8-9: Find the indicated term and the general term of the Geometric Sequence
- Examples #10-13: Determine if the sequence is Arithmetic, Geometric or neither
- Example #14: Determine if the sequence is Arithmetic, Geometric or neither
- Recursive Formula for Arithmetic Sequences
- Examples #15-18: Find the General Term and the Recursive Formula for the Arithmetic Sequence
- Example #19: Discovering the Fibonacci Sequence
Summation Notation
53 min 13 Examples
- Introduction to Video: Series and Summation Notation
- Series Overview and Examples #1-2: Find the Sum of the first four terms
- Finite and Infinite Series with Examples #3-5: Evaluate each Series
- Examples #6-9: Evaluate the Series
- Summation Properties
- Examples #10-11: Evaluate the Series using Summation Properties
- Examples #12-13: Write using Sigma Summation Notation and Show how to Reindex the Series
Geometric Series
50 min 15 Examples
- Introduction to Video: Arithmetic and Geometric Series
- Overview of the Arithmetic Series with Example #1
- Examples #2-3: Find the Sum of the Arithmetic Series
- Examples #4-5: Find the First Term and Common Difference given the Sum of the Arithmetic Series
- Overview of the Geometric Series with Examples #6-7
- Overview of the Infinite Geometric Series
- Examples #8-11: Find the Sum of the Infinite Geometric Series
- Examples #12-15: Determine if the Infinite Geometric Series will Converge or Diverge
Mathematical Induction
53 min 5 Examples
- Introduction to Video: Proof by Mathematical Induction
- Principle of Mathematical Induction and our Three Step Process
- Examples #1-3: Prove by Induction the Algebraic Formula
- Examples #4-5: Prove by Induction the Summation Formula
Binomial Theorem
56 min 7 Examples
- Introduction to Video: The Binomial Theorem and Pascal’s Triangle
- Overview of the Binomial Theorem and Binomial Coefficients
- Examples #1-2: Evaluate the Binomial Coefficient
- Binomial Expansion Theorem and Example #3
- Examples #4-6: use the Binomial Theorem to expand the binomial
- Overview of Pascal’s Triangle
- Example #7: Use Pascal’s Triangle to expand the binomial
Chapter Test
1 hr 33 min 21 Examples
- Examples #1-5: Find the first five terms of the Sequence and determine if Arithmetic, Geometric or neither
- Example #6: Find the indicated terms of the Arithmetic Sequence
- Example #7: Find the indicated terms of the Arithmetic Series
- Example #8: Find the indicated terms of the Geometric Sequence
- Examples #9-17: Evaluate the Series
- Examples #18-19: Use the Binomial Theorem to expand
- Examples #20-21: Use the Principle of Mathematical Induction
