   Chapter 9.7, Problem 40ES ### 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

# For every integer n ≥ 0 and for every nonnegative real number x , 1 + n x ≤ ( 1 + x ) x .

To determine

To prove that for every integer n0 and for every nonnegative real number x, 1+nx(1+x)n.

Explanation

Given:

The integer n0.

Proof:

Consider; 1+nx(1+x)n

For n=0 ;

Left side=1+(0)x=1Right side=(1+x)0=1

Therefore, Left side=1=Right side.

Hence the result is true for n=0.

For n=1 ;

Left side=1+(1)x=1+xRight side=(1+x)1=1+x

Therefore, Left side=Right side=1+x.

Hence, the result is true for n=0.

For n=2 ;

Left side=1+(2)x=1+2x

Right side=(1+x)2=1+2x+x2

Therefore, Left side<Right side.

Hence, the result is true for n=2

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 