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…
Mathematical Induction
Mathematical Induction
Mathematical Induction
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 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
Example 1 (cont)
Example 1 (cont)
Example 1 (cont)
Example 1 (cont)
Proving an Equality Statement using Mathematical Induction Example 2