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3) Prove by induction that n²>2n + 3 for every integer n >3

3) Prove by induction that n²>2n + 3 for every integer n >3

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Sequences And Series
Section8.5: Mathematical Induction
Problem 1E: Mathematical induction is a method of proving that a statement P(n) is true for all ________ numbers...
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Prove the following: 3) Prove by induction that n² ≥ 2n + 3 for every integer n >3 4) Prove by induction that n² + n + 1 is odd for every nonnegative integer n (hint: you can assume any number in the form 2k+2 is even)
Transcribed Image Text:Prove the following: 3) Prove by induction that n² ≥ 2n + 3 for every integer n >3 4) Prove by induction that n² + n + 1 is odd for every nonnegative integer n (hint: you can assume any number in the form 2k+2 is even)
Mathematical Induction is a proof technique used to prove the statement in the form: Vn E N, P (n) There are two parts to a proof by induction: Basis Step: Show P(n) is true if P(1) is true Inductive Step: Show the statement Vk € N, P(k) ⇒ P(k + 1) is true
Transcribed Image Text:Mathematical Induction is a proof technique used to prove the statement in the form: Vn E N, P (n) There are two parts to a proof by induction: Basis Step: Show P(n) is true if P(1) is true Inductive Step: Show the statement Vk € N, P(k) ⇒ P(k + 1) is true
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