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Use the PMI to prove that 3-1 is even for all n E N.

Use the PMI to prove that 3-1 is even for all n E N.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 85E
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Use the PMI to prove that 3 - 1 is even for all n E N. Proof. Base case: Since 3¹ - 1 = 2, which is even. Thus the statement is true for n = [Select] Inductive step: Assume that there is a natural number n such that 3 - 1 is even. Then 3-1 = [Select] for some integer k. Then 3" [Select] ✓. On both sides, first multiply by 3, then subtract 1, and simplify to get 3+1 -1 = 2( [Select] which is an [Select] integer. Hence, by the PMI, 3 - 1 is even for all n E N. )
Transcribed Image Text:Use the PMI to prove that 3 - 1 is even for all n E N. Proof. Base case: Since 3¹ - 1 = 2, which is even. Thus the statement is true for n = [Select] Inductive step: Assume that there is a natural number n such that 3 - 1 is even. Then 3-1 = [Select] for some integer k. Then 3" [Select] ✓. On both sides, first multiply by 3, then subtract 1, and simplify to get 3+1 -1 = 2( [Select] which is an [Select] integer. Hence, by the PMI, 3 - 1 is even for all n E N. )
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