Use the PMI to prove that 3-1 is even for all n E N.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![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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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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