Mathematical Induction Thinking Skill: Develop Confidence in Reason Warm Up: Find the k+1 term (P k+1 ) 1) 2)

Need for Induction: For the sequence 1, 3, 5, 7, 9,…. Find S 1 = S 2 = S 3 = S 4 = What does S n equal?

Deductive Proofs Start with one given fact, then using definitions, axioms & theorems build upon that given statement to create another and another until you get the final statement you want. Hard to use to prove/create sequence & series formulas.

Inductive Proofs Show something is true for P 1. Then show that if P k is true then P k+1 must be true. Like the domino effect.

Examples Prove that …. + (2n – 1) = n 2

Examples Prove that …. + (4n – 1) = n(2n +1)

Examples Prove that … +(8n – 5) = n(4n – 1)

Examples Find a formula for the sum of the first n terms of the below sequence. Use mathematical induction to verify your formula.

Examples Find a formula for the sum of the first n terms of the below sequence. Use mathematical induction to verify your formula. 1, 5, 9, 13, …

Examples Find a formula for the sum of the first n terms of the below sequence. Use mathematical induction to verify your formula. 25, 22, 19, 16,…