For every natural number n, one of n-1, n, or n+1 is a multiple of 3
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.5: Mathematical Induction
Problem 31E
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Question
For every natural number n, one of n-1, n, or n+1 is a multiple of 3
Expert Solution
Step 1
The following two steps are used to prove a statement P(n) by the principle of mathematical induction.
- Basis step: Show that the statement P(n) is true for the initial values of n.
- Inductive step: Assume that the statement P(n) is true for n=k. Then, prove that the statement P(n) is true for n=k+1, that is, if P(k) is true then verify P(k+1) is true.
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