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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

15-24 Proving a statement Use mathematical induction to show that the given statement is true.

n 2 + n is divisible by 2 for all natural numbers n

To determine

To prove:

n2+n is divisible by 2 for all natural numbers n.

Explanation

Given:

n2+n

Approach:

Suppose the following conditions are satisfied.

1) P(1) is true.

2) For every natural number k, if P(k) is true then P(k+1) is true.

Then P(n) is true for all natural numbers n.

Calculation:

Let P(n)=n2+n

For n=1

P(1)=12+1=2

which is divisible by 2.

Let the statement is true for n=k, then

P(k)=k2+k is divisible by 2

Let n=k+1

P(k+1)=(k+1)

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Chapter 13 Solutions

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