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**Lesson 10.4: Mathematical Induction**

Mathematical Induction is a form of mathematical proof. Principle of Mathematical Induction: Let Pn be a statement involving a positive integer, n. If P1 is true, and The truth of Pk implies the truth of Pk+1, for every positive integer k, then Pn is true for all integers n. [p 688] To apply Mathematical Induction you need to Show the statement is true when n=1 Assume the statement is true for n=k, and then use it to show the statement is true for n=k+1.

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**1. Let n = , show the statement is true. 1**

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

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**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. Must show that

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**Mathematical Induction Proofs - Worksheet**

Homework: p693: #11, 15, 17, 21

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To prove by induction that (1 + x) n ≥ 1 + nx for x > -1, n N Next (c) Project Maths Development Team 2011 Note: x>-1. Hence (1+x)>0.

To prove by induction that (1 + x) n ≥ 1 + nx for x > -1, n N Next (c) Project Maths Development Team 2011 Note: x>-1. Hence (1+x)>0.

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