**Series and Sequences**

## 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 #5-7: Write the first five terms of the sequence
- Examples #8-9: Write the first five terms of the sequence
- Examples #10-12: Simplify the Factorial Expression
- Examples #13-15: Simplify the Factorial Expression
- Examples #16-17: Write the first four terms of the sequence
- Examples #18-19: Graph the Sequence
- Examples #20-21: Determine if the Sequence is Monotonic
- Examples #22-23: 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 #10-11: Determine if the sequence is Arithmetic, Geometric or neither
- Examples #12-13: Determine if the sequence is Arithmetic, Geometric or neither
- Examples #14: Determine if the sequence is Arithmetic, Geometric or neither
- Recursive Formula for Arithmetic Sequences
- Examples #15-16: Find the General Term and the Recursive Formula for the Arithmetic Sequence
- Examples #17-18: Find the General Term and the Recursive Formula for the Geometric 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 #6-8: Evaluate the Series
- Example #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
- Example #4: Find the First Term and Common Difference given the Sum of the Arithmetic Series
- Example #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 #8-9: Find the Sum of the Infinite Geometric Series
- Examples #10-11: Find the Sum of the Infinite Geometric Series
- Examples #12-13: Determine if the Infinite Geometric Series will Converge or Diverge
- Examples #14-15: 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
- Example #1: Prove by Induction the Algebraic Formula
- Example #2: Prove by Induction the Algebraic Formula
- Example #3: Prove by Induction the Algebraic Formula
- Example #4: Prove by Induction the Summation Formula
- Example #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
- Example #4: use the Binomial Theorem to expand the binomial
- Example #5: use the Binomial Theorem to expand the binomial
- Example #6: use the Binomial Theorem to expand the binomial
- Overview of Pascal’s Triangle
- Example #7: Use Pascal’s Triangle to expand the binomial