   Chapter 11.2, Problem 41ES ### 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: If c is a positive real number and f ( n ) = c for every integer n ≥ 1 . then f ( n ) is Θ ( 1 ) .

To determine

To prove:

That f(n) isΘ(1) for every n1, where f(n)=c and c is a positive real number.

Explanation

Given information:

c is any positive real number such that for every n1, f(n)=c

Formula used:

Let f and g be real valued functions defined on the same nonnegative integers, with g(n)0 for every integer nr, where r is positive real number.

Then,

f is of order g, written f(n) is Θ(g(n)), if and only if, there exist positive real numbers A,B and kr such that

Ag(n)f(n)Bg(n) for every integer ka.

Proof:

Let A and B be any positive real numbers such that Ac and Bc

### 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 