   Chapter 1, Problem 17P ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Prove that if n is a positive integer, then 7n ‒ 1 is divisible by 6.

To determine

To prove: If n is positive integer, then 7n1 is divisible by 6.

Explanation

Proof:

Use mathematical induction on n.

Let Sn be the statement 7n1 is divisible by 6

Base case: n=1

To prove that the statement is true for n=1.

711=6

Clearly, it is divisible by 6.

Therefore, the statement is true for n=1.

Induction hypothesis: n=k

Assume that the claim is true for n=k.

That is, 7k1=6m, for some positive integer m

Thus 7k=6m+1.

Inductive step: n=k+1

To prove that the statement is true for n=k+1

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 