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Suppose we want to use mathematical induction to prove that for each natural number n, n(3n – 1) 2 +5+8+ + (3n – 1) = ... 2 In our induction step, what would we assume to be true and what do we wish to show: a. None of the above (k + 1)(3 (k + 1) –- 1) + (3k – 1) + (3 (k – 1) – 1) = Assume 2 + 5 +8+ ... 2 b. k (3k – 1) WTS: 2 +5 +8+ . + (3k – 1) = ... 2 k (3k - 1) Assume 2 +5 +8+ . + (3k – 1) = 2 C. WTS: 2 +5 +8+ - + (3k – 1) + (3(k + 1) – 1) = k+ 1) (3 (k + 1) – 1) ... 3k Assume 2 - 3 -8 - .. - (3k + 1) = 2 d. 3 (k + 1) WTS: 2 – 3 - 8- . - (3 (k – 1) – 1) = ...

Suppose we want to use mathematical induction to prove that for each natural number n, n(3n – 1) 2 +5+8+ + (3n – 1) = ... 2 In our induction step, what would we assume to be true and what do we wish to show: a. None of the above (k + 1)(3 (k + 1) –- 1) + (3k – 1) + (3 (k – 1) – 1) = Assume 2 + 5 +8+ ... 2 b. k (3k – 1) WTS: 2 +5 +8+ . + (3k – 1) = ... 2 k (3k - 1) Assume 2 +5 +8+ . + (3k – 1) = 2 C. WTS: 2 +5 +8+ - + (3k – 1) + (3(k + 1) – 1) = k+ 1) (3 (k + 1) – 1) ... 3k Assume 2 - 3 -8 - .. - (3k + 1) = 2 d. 3 (k + 1) WTS: 2 – 3 - 8- . - (3 (k – 1) – 1) = ...

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.3: Divisibility
Problem 44E
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Suppose we want to use mathematical induction to prove that for each natural number n, n(3n – 1) 2 +5+8+ + (3n – 1) = ... 2 In our induction step, what would we assume to be true and what do we wish to show: a. None of the above (k + 1)(3 (k + 1) –- 1) + (3k – 1) + (3 (k – 1) – 1) = Assume 2 + 5 +8+ ... 2 b. k (3k – 1) WTS: 2 +5 +8+ . + (3k – 1) = ... 2 k (3k - 1) Assume 2 +5 +8+ . + (3k – 1) = 2 C. WTS: 2 +5 +8+ - + (3k – 1) + (3(k + 1) – 1) = k+ 1) (3 (k + 1) – 1) ... 3k Assume 2 - 3 -8 - .. - (3k + 1) = 2 d. 3 (k + 1) WTS: 2 – 3 - 8- . - (3 (k – 1) – 1) = ...
Transcribed Image Text:Suppose we want to use mathematical induction to prove that for each natural number n, n(3n – 1) 2 +5+8+ + (3n – 1) = ... 2 In our induction step, what would we assume to be true and what do we wish to show: a. None of the above (k + 1)(3 (k + 1) –- 1) + (3k – 1) + (3 (k – 1) – 1) = Assume 2 + 5 +8+ ... 2 b. k (3k – 1) WTS: 2 +5 +8+ . + (3k – 1) = ... 2 k (3k - 1) Assume 2 +5 +8+ . + (3k – 1) = 2 C. WTS: 2 +5 +8+ - + (3k – 1) + (3(k + 1) – 1) = k+ 1) (3 (k + 1) – 1) ... 3k Assume 2 - 3 -8 - .. - (3k + 1) = 2 d. 3 (k + 1) WTS: 2 – 3 - 8- . - (3 (k – 1) – 1) = ...
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