   Chapter 13.5, Problem 24E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

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

# SKILLS 1 5 − 2 4 Proving a Statement Use mathematical induction to show that the given statement is true. 100 n ≤ n 2 for all n ≥ 100 .

To determine

To prove:

100nn2 for all n100.

Explanation

Approach:

Principal of Mathematical Induction:

Suppose P(n) is a statement depending on every natural number n and 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:

Suppose,

P(n)=100nn2(1)

For all n100

Step 1 Show that P(100) is true.

Substitute 100 for n in equation (1).

100(100)(100)2, which is true.

Thus, P(100) is true.

Step 2 Assume that P(k) is true.

So,

100kk2

k2100k(2)

Step 3 Show that it is true for P(k+1)

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