4. Use mathematical induction to prove the truth of each of the following assertions for all n ≥ 1. (a) [BB] n³ + 2n is divisible by 3. (b) n³ + (n + 1)³ + (n + 2)3 is divisible by 9. (c) [BB] 5" - 1 is divisible by 4. (d) 8"-3" is divisible by 5. (e) 52n - 25n is divisible by 7. [BB] 10+1 + 10 + 1 is divisible by 3. (g) n³ +5n is divisible by 6. (h) on I 2n 5n is divisible by 6
4. Use mathematical induction to prove the truth of each of the following assertions for all n ≥ 1. (a) [BB] n³ + 2n is divisible by 3. (b) n³ + (n + 1)³ + (n + 2)3 is divisible by 9. (c) [BB] 5" - 1 is divisible by 4. (d) 8"-3" is divisible by 5. (e) 52n - 25n is divisible by 7. [BB] 10+1 + 10 + 1 is divisible by 3. (g) n³ +5n is divisible by 6. (h) on I 2n 5n is divisible by 6
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.2: Mathematical Induction
Problem 46E: Use generalized induction and Exercise 43 to prove that n22n for all integers n5. (In connection...
Related questions
Question
Q4 e and g
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage