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DISCUSS: True or False? Determine whether each statement is true or false. If you think the statement is true, prove it. If you think it is false, give an example in which it fails. (a) p(n) = n² – n + 11 is prime for all n. (b) n >n for all n2 2. (c) 22n+1 + 1 is divisible by 3 for all n21. (d) n 2 (n + 1)² for all n 2 2. (e) n - n is divisible by 3 for all n2 2. (f) n - 6n? + 1ln is divisible by 6 for all n2 1.

DISCUSS: True or False? Determine whether each statement is true or false. If you think the statement is true, prove it. If you think it is false, give an example in which it fails. (a) p(n) = n² – n + 11 is prime for all n. (b) n >n for all n2 2. (c) 22n+1 + 1 is divisible by 3 for all n21. (d) n 2 (n + 1)² for all n 2 2. (e) n - n is divisible by 3 for all n2 2. (f) n - 6n? + 1ln is divisible by 6 for all n2 1.

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Sequences And Series
Section8.5: Mathematical Induction
Problem 37E
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DISCUSS: True or False? Determine whether each statement is true or false. If you think the statement is true, prove it. If you think it is false, give an example in which it fails. (a) p(n) = n² – n + 11 is prime for all n. (b) n >n for all n2 2. (c) 22n+1 + 1 is divisible by 3 for all n21. (d) n 2 (n + 1)² for all n 2 2. (e) n - n is divisible by 3 for all n2 2. (f) n - 6n? + 1ln is divisible by 6 for all n2 1.
Transcribed Image Text:DISCUSS: True or False? Determine whether each statement is true or false. If you think the statement is true, prove it. If you think it is false, give an example in which it fails. (a) p(n) = n² – n + 11 is prime for all n. (b) n >n for all n2 2. (c) 22n+1 + 1 is divisible by 3 for all n21. (d) n 2 (n + 1)² for all n 2 2. (e) n - n is divisible by 3 for all n2 2. (f) n - 6n? + 1ln is divisible by 6 for all n2 1.
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