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Lesson 10.4: Mathematical Induction Mathematical Induction is a form of mathematical proof. Principle of Mathematical Induction: Let P n be a statement.

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Presentation on theme: "Lesson 10.4: Mathematical Induction Mathematical Induction is a form of mathematical proof. Principle of Mathematical Induction: Let P n be a statement."— Presentation transcript:

1 Lesson 10.4: Mathematical Induction Mathematical Induction is a form of mathematical proof. Principle of Mathematical Induction: Let P n be a statement involving a positive integer, n. If 1.P 1 is true, and 2.The truth of P k implies the truth of P k+1, for every positive integer k, then P n is true for all integers n. [p 688] To apply Mathematical Induction you need to 1.Show the statement is true when n=1 2.Assume the statement is true for n=k, and then use it to show the statement is true for n=k+1.

2 Use Mathematical Induction to prove the statement is true positive integer. 1. Let n =, show the statement is true. 2a. Let n =, assume the statement below is true. 2b. Let n =, show the statement is true, using 2a. 1 k k+1 Must show that = S k

3 Use Mathematical Induction to prove the statement is true positive integer. P693 #18: 1. Let n =, show the statement is true. 2a. Let n =, assume the statement below is true. 2b. Let n =, show the statement is true, using 2a. Must show that

4 Mathematical Induction Proofs - Worksheet Homework: p693: #11, 15, 17, 21


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