×
Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 5.4 - Problem 23e
Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 5.4 - Problem 23e

×

# Devise a recursive algorithm for computing n2 where n is a

ISBN: 9780073383095 37

## Solution for problem 23E Chapter 5.4

Discrete Mathematics and Its Applications | 7th Edition

• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants

Discrete Mathematics and Its Applications | 7th Edition

4 5 1 430 Reviews
18
4
Problem 23E

Problem 23E

Devise a recursive algorithm for computing n2 where n is a nonnegative integer, using the fact that (n + 1)2 = n2 + 2n + 1. Then prove that this algorithm is correct.

Step-by-Step Solution:
Step 1 of 3

Discrete Mathematics CS225 Terms and concepts: Week 2 Reading 145-159, 165-167. 183-184. 201-203 and Lectures and Supplemental Info List of Types of Numbers: • Natural numbers ( ℕ ): Counting numbers. {0, 1, 2, 3…} • Integers ( ℤ ): Positive and negative counting numbers. {…-2, -1, 0, 1, 2, …} • Rational numbers ( ℚ ): Numbers that can be expressed as a ratio of an integer to a non-zero integer. ◦ Quotients of integers. ◦ All integers are rational, but not all rational numbers are integers. • Real numbers ( ℝ ) : Numbers that have decimal representations. ◦ Can be positive, negative, or zero. ◦ All rational numbers are real, not all real numbers are rational. • Irrational numbers (I): Real numbers that are not rational. Elementary Number Theory and Methods of Proof • Theorem:Amathematical statement that is true. • Proof:Arigorous argument that a theorem is true. • Formal Proof: Manipulate logic expressions via mechanical rules of inference. ◦ Computers produce these. • Informal Proof:Argument stated in natural language. ◦ The argument must still be rigorous and sound. ◦ Mathematicians produce these. • An example involving a concept used frequently in CS. ◦ Floor of x ( ⌊x⌋ ): Greatest integer of x. The largest integer that is less than or equal to x. ▪ On the number line, ⌊x⌋ is the integer immediately to the left of x (or equal to x if x itself is an integer). • Ex: ◦ ⌊2.3⌋=2

Step 2 of 3

Step 3 of 3

##### ISBN: 9780073383095

The full step-by-step solution to problem: 23E from chapter: 5.4 was answered by , our top Math solution expert on 06/21/17, 07:45AM. This full solution covers the following key subjects: Algorithm, Integer, correct, devise, fact. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. Since the solution to 23E from 5.4 chapter was answered, more than 435 students have viewed the full step-by-step answer. The answer to “Devise a recursive algorithm for computing n2 where n is a nonnegative integer, using the fact that (n + 1)2 = n2 + 2n + 1. Then prove that this algorithm is correct.” is broken down into a number of easy to follow steps, and 33 words. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7.

## Discover and learn what students are asking

Calculus: Early Transcendental Functions : Riemann Sums and Definite Integrals
?In Exercises 3–8, evaluate the definite integral by the limit definition. $$\int_{1}^{4} 4 x^{2} d x$$

Statistics: Informed Decisions Using Data : Comparing Three or More Means (One-Way Analysis of Variance)
?The acronym ANOVA stands for _________ __ ______.

#### Related chapters

Unlock Textbook Solution