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

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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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