Q. For each positive integer n, let P(n) be the property 5n – 1 is divisible by 4. a. Write P(0). Is P(0) true? b. Write P(k). c. Write P(k + 1). d. In a proof by mathematical induction that this divisibility property holds for all integers n>0, what must be shown in the inductive step?

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.4: Mathematical Induction
Problem 2ECP
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Q. For each positive integer n, let P(n) be the
property 5n – 1 is divisible by 4.
a. Write P(0). Is P(0) true?
b. Write P(k).
c. Write P(k + 1).
d. In a proof by mathematical induction that this divisibility
property holds for all integers n>0, what must be shown
in the inductive step?
Transcribed Image Text:Q. For each positive integer n, let P(n) be the property 5n – 1 is divisible by 4. a. Write P(0). Is P(0) true? b. Write P(k). c. Write P(k + 1). d. In a proof by mathematical induction that this divisibility property holds for all integers n>0, what must be shown in the inductive step?
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