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

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Sequences And Series
Section8.6: The Binomial Theorem
Problem 54E
icon
Related questions
Question
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
Expert Solution
steps

Step by step

Solved in 3 steps with 1 images

Blurred answer
Recommended textbooks for you
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning