Explanation Given: Statements says the series n 2 − n + 41 is a prime number is true for n = 1 but not true for n = 41 . Formula used: The Principle of Mathematical Induction Suppose that the following two conditions are satisfied with regard to a statement about natural numbers: CONDITION I: The statement is true for the natural number 1. CONDITION II: If the statement is true for some natural number k , it is also true for the next natural number k + 1 . Then the statement is true for all natural numbers. Proof: Consider the statement n 2 − n + 41 is a prime number is true for n = 1 but not true for n = 41 -----(1) Step 1: Show that statement (1) is true for the natural number n = 1 ...

10th Edition

ISBN: 8220101460912

Author: Sullivan

Publisher: PEARSON

See similar textbooks

Concept explainers

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

Videos

Question

Chapter 12.4, Problem 28AYU

To determine

To prove: The given statement $n^{2} - n + 41$ is a prime number is true for $n = 1$ but not true for $n = 41$ using the Principle of Mathematical Induction.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.4, Problem 27AYU

Chapter 12.4, Problem 29AYU

Students have asked these similar questions

1) Find the equation of the tangent line to the graph y=xe at the point (1, 1).

3) Suppose that f is differentiable on [0, 5], and f'(x) ≤ 3 over this interval. If f(0) = −1, what is the maximum possible value of f(5)?

2) Find the maximum value of f(x, y) = x - y on the circle x² + y² - 4x - 2y - 4 = 0.

Chapter 12 Solutions

EBK PRECALCULUS

Ch. 12.1 - For the function f( x )= x1 x , find f( 2 ) and f(...Ch. 12.1 - True or False A function is a relation between two...Ch. 12.1 - Prob. 3AYU Ch. 12.1 - True or False The notation a 5 represents the...Ch. 12.1 - True or False If is am integer, then Ch. 12.1 - The sequence a 1 =5 , a n =3 a n1 is an example of...Ch. 12.1 - The notation a 1 + a 2 + a 3 ++ a n = k=1 n a k...Ch. 12.1 - Prob. 8AYU Ch. 12.1 - In Problems 11-16, evaluate each factorial...Ch. 12.1 - Prob. 10AYU

Additional Math Textbook Solutions

Find more solutions based on key concepts

In hypothesis testing, the common level of significance is =0.05. Some might argue for a level of significance ...

Basic Business Statistics, Student Value Edition

Fill in each blank so that the resulting statement is true. If n is a counting number, bn, read ______, indicat...

College Algebra (7th Edition)

CHECK POINT I You deposit $1000 in a saving account at a bank that has a rate of 4%. a. Find the amount, A, of ...

Thinking Mathematically (6th Edition)

In Exercises 13–16, find the margin of error for the values of c, ?, and n. 16. e = 0.975, ? = 4.6, n = 100

Elementary Statistics: Picturing the World (7th Edition)

Fill in each blank so that the resulting statement is true. An equation that expresses a relationship between t...

Algebra and Trigonometry (6th Edition)

Testing Claims About Proportions. In Exercises 7–22, test the given claim. Identify the null hypothesis, altern...

Elementary Statistics (13th Edition)

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

To prove: The given statement n 2 − n + 41 is a prime number is true for n = 1 but not true for n = 41 using the Principle of Mathematical Induction.

Solution Summary: The author explains the Principle of Mathematical Induction, which states that the statement is true for n = 1, but not true, for all natural numbers.

Concept explainers

Videos

To prove: The given statement $n^{2} - n + 41$ is a prime number is true for $n = 1$ but not true for $n = 41$ using the Principle of Mathematical Induction.

Want to see the full answer?

Chapter 12 Solutions

Additional Math Textbook Solutions

To prove: The given statement n 2 − n + 41 is a prime number is true for n = 1 but not true for n = 41 using the Principle of Mathematical Induction.

Solution Summary: The author explains the Principle of Mathematical Induction, which states that the statement is true for n = 1, but not true, for all natural numbers.

Concept explainers

Videos

To prove: The given statement n2 − n + 41 is a prime number is true for n = 1 but not true for n = 41 using the Principle of Mathematical Induction.

Want to see the full answer?

Chapter 12 Solutions

Additional Math Textbook Solutions

To prove: The given statement $n^{2} - n + 41$ is a prime number is true for $n = 1$ but not true for $n = 41$ using the Principle of Mathematical Induction.