   Chapter 11.4, Problem 43ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
1 views

# Prove by mathematical induction that n ≥ 10 n for every integer n ≥ 1 .

To determine

To prove:

Prove by mathematical induction that n = 10nfor all integers n = 1.

Explanation

Given information:

n = 10nfor all integers n = 1.

Proof:

PROOF BY INDUCTION:

Let P(n) be "n10n"

Basis step: n = 1

n=110n=101=10

Thus P (1) is true as 110.

Inductive step:

Let P(k) be true, thus k10k with k2

We need to prove that P ( k + 1) is true.

k+110k+1                            Since P(k) is true

10k+10k                            110k as k2

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