Book 10:  Sequences, Series and Induction 

You Will

 
Subjects

 

Chapter 1

Chapter 2

Chapter 3

Chapter 4

Appendix

  • Arithmetic Sequences

  • Natural Sequences

  • Arithmetic Series

  • Mathematical Induction

  • Kid Stuff

  • Those Darn Rabbits

  • Traveling man

  • Sicilian Bounty

 

 

Video Highlights

Nature is full of patterns involving number sequences. This book introduces arithmetic and natural sequences and uses sequences to demonstrate the procedure of mathematical statements are always true. Examples include the projection of a child’s final adult height and occurrences of the Fibonnaci sequence in nature.

 

Chapter 1

Chapter 2

Chapter 3

Chapter 4

  • Sequence Defined

  • Arithmetic Sequences

  • A Practical Example

  • A General Formula

  • The Fibonacci Sequence

  • Getting Serious About Series

  • A Helpful Formula

  • Mathematical Induction

  • Another Proof

  • Importance of Induction Step

  • One Formula Fits All

  • A Counterexample

 

 

Summary/Terminology

 

Sequence
Arithmetic Sequence
Common Difference
Finite Sequence
Infinite Sequence
Ellipsis
Formula for an
an
General Term Formula
Recursive Formula
Natural Sequences

Fibonacci Sequence
Golden Ratio
Arithmetic Series
Sigma 
Sum of Finite Arithmetic Sequences
Combined Formula
Principle of Mathematical Induction
Proof by Mathematical Induction
Counterexample