9.4 Proof by Mathematical Induction-1

9.4 Proof by Mathematical Induction-1 - 9.4 Proof by...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 9.4 Proof by Mathematical Induction Friday, November 04, 2011 6:47 AM Agenda: 1. Lesson: 9.4 Proof by Mathematical Induction Lesson: 9.4 Proof by Mathematical Induction Goal: Prove summations by mathematical induction. DOD Principals of Mathematical Induction Let be a statement involving the positive integer . If: 1. is true (the base case) 2. Implying that is true shows that is also true, for every positive Then value, must be true for all positive integers . Our steps… 1. Show that is true (prove the base case) (this is usually trivial, but necessary!) 2. Assume is true. Using the fact that is assumed true, show that is also true. (this step is harder than 1., but with some algebraic manipulation, it is possible) Hint • Think of Why Proofs by Induction? • It is not enough to show that patterns hold. Do they hold up for every value of the variable, or just the ones you tried? How do you know they will hold up for every value of the variable. Proofs by Induction can be thought of as showing that an infinite line of dominoes will fall if you can prove these two cases. • The first domino will fall. Ch_9 Page 1 • The first domino will fall. • Any domino will make another domino fall. Examples Find for the given . (substitute Prove by mathematical induction 1. Show that is true 2. Assume is true. Show that Ch_9 Page 2 for is also true. and simplify) Ch_9 Page 3 Ch_9 Page 4 ...
View Full Document

This note was uploaded on 11/19/2011 for the course MATH 180 taught by Professor Byrns during the Spring '11 term at Montgomery College.

Ask a homework question - tutors are online