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 ...

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Author: Sullivan

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Chapter 12.4, Problem 28AYU

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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.

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Chapter 12.4, Problem 27AYU

Chapter 12.4, Problem 29AYU

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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.

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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.

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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.