When proving by induction that an inequality P(n):an

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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N
k
k+1
When proving by induction that an inequality nNk+1a only ca ba
some natural number N, what is crucial in the induction step?
based on a bP(n):a" holds for all n greater than
c
When proving by induction that an inequality P(n):an <bn holds for all n greater than
some natural number N, what is crucial in the induction step?
a) Showing that ak+1 <bk+1 based on ak <bk
b) Proving that aN <b only
c) Demonstrating that the inequality flips for k+1
d) Using a direct proof for each case
Transcribed Image Text:N k k+1 When proving by induction that an inequality nNk+1a only ca ba some natural number N, what is crucial in the induction step? based on a bP(n):a" holds for all n greater than c When proving by induction that an inequality P(n):an <bn holds for all n greater than some natural number N, what is crucial in the induction step? a) Showing that ak+1 <bk+1 based on ak <bk b) Proving that aN <b only c) Demonstrating that the inequality flips for k+1 d) Using a direct proof for each case
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