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2. 1.2+2.3+3.4 + ... + n(n + 1) = n(n + 1)(n+ 2) 3. for any n e N 2+ 22 + 2+. 3 + 2n = 2n+1 -2 for anynsN 4.

2. 1.2+2.3+3.4 + ... + n(n + 1) = n(n + 1)(n+ 2) 3. for any n e N 2+ 22 + 2+. 3 + 2n = 2n+1 -2 for anynsN 4.

Calculus: Early Transcendentals
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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Prove the following using mathematical induction. 1. 3. 1.2+2.3 + 3 4 + ... + n(n + 1) = nn + 1n+21 for any n e N 3 2 + 22 + 23 +... + 2" = 2n*1 – 2, for any n eN 4. 5. 1+8+ 16 +... + 8(n – 1) = (2n – 1)2, for any n e N n(n +3) n(n + 1)(n + 2) 4(n + 1)(n + 2)' 6. 1 + 1.2.3 2.3·43.4.5 for any neN ... 7. n? > 2n, for any positive integer n23 8. 3"- 2 2 10n, for any positive integer n 2 4 9. 4° -1 is divisible by 3 for any neN TA BA 10. n° + 3n? + 2n is divisible by 6 for any n eN 2.
Transcribed Image Text:Prove the following using mathematical induction. 1. 3. 1.2+2.3 + 3 4 + ... + n(n + 1) = nn + 1n+21 for any n e N 3 2 + 22 + 23 +... + 2" = 2n*1 – 2, for any n eN 4. 5. 1+8+ 16 +... + 8(n – 1) = (2n – 1)2, for any n e N n(n +3) n(n + 1)(n + 2) 4(n + 1)(n + 2)' 6. 1 + 1.2.3 2.3·43.4.5 for any neN ... 7. n? > 2n, for any positive integer n23 8. 3"- 2 2 10n, for any positive integer n 2 4 9. 4° -1 is divisible by 3 for any neN TA BA 10. n° + 3n? + 2n is divisible by 6 for any n eN 2.
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