Mathematical Induction Lesson 1 3 Mathematical Induction is

  • Slides: 20
Download presentation
Mathematical Induction Lesson 1 -3

Mathematical Induction Lesson 1 -3

Mathematical Induction is a form of a mathematical proof. Just because a rule, pattern,

Mathematical Induction is a form of a mathematical proof. Just because a rule, pattern, or formula seems to work for several values of n, you cannot simply decide that it is valid for all values of n without going through a legitimate proof!

Why I Don’t Trust Patterns…

Why I Don’t Trust Patterns…

Why I Don’t Trust Patterns…

Why I Don’t Trust Patterns…

Why I Don’t Trust Patterns…

Why I Don’t Trust Patterns…

Why I Don’t Trust Patterns…

Why I Don’t Trust Patterns…

Why I Don’t Trust Patterns…

Why I Don’t Trust Patterns…

Why I Don’t Trust Patterns…

Why I Don’t Trust Patterns…

Mathematical Induction

Mathematical Induction

Mathematical Induction

Mathematical Induction

Mathematical Induction

Mathematical Induction

Mathematical Induction The Principle of Mathematical Induction Let Pn be a statement involving the

Mathematical Induction The Principle of Mathematical Induction Let Pn be a statement involving the positive integer n. If 1. P 1 is true, and 2. the truth of Pk implies the truth of Pk+1 , for every positive integer k, then Pn must be true for all integers n.

Mathematical Induction Proof by Mathematical Induction Step 1: Prove that the statement is true

Mathematical Induction Proof by Mathematical Induction Step 1: Prove that the statement is true for n = 1 Step 2: Assume that the statement is true for n = k Step 3: Show that it is true for n = k + 1 This will then prove that the statement is always true for every positive integer n.

Proving an Equality Statement using Mathematical Induction Example 1

Proving an Equality Statement using Mathematical Induction Example 1

Example 1 (cont)

Example 1 (cont)

Example 1 (cont)

Example 1 (cont)

Example 1 (cont)

Example 1 (cont)

Example 1 (cont)

Example 1 (cont)

Proving an Equality Statement using Mathematical Induction Example 2

Proving an Equality Statement using Mathematical Induction Example 2

Example 2

Example 2