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
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Q4 e and g
![4. Use mathematical induction to prove the truth of each of
the following assertions for all n ≥ 1.
3
(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.
(f) [BB] 10+1 + 10 + 1 is divisible by 3.
(g) n³ +5n is divisible by 6.
(h) on
2n 5n is divisible by 6
diary](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F16cd84dd-3536-4a60-93ca-72803276df73%2F3fab47a0-56b3-4b5b-9658-f20fe8274594%2F9hen2d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Use mathematical induction to prove the truth of each of
the following assertions for all n ≥ 1.
3
(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.
(f) [BB] 10+1 + 10 + 1 is divisible by 3.
(g) n³ +5n is divisible by 6.
(h) on
2n 5n is divisible by 6
diary
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