Explanation Given: Statements says the series n ( n + 1 ) ( n + 2 ) is divisible by 6 is true for all natural number. 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 ( n + 1 ) ( n + 2 ) is divisible by 6 -----(1) Step 1: Show that statement (1) is true for the natural number n = 1 . That is 1 ( 1 + 1 ) ( 1 + 2 ) = 6 is divisible by 6. Hence the statement is true for the natural number n = 1 . Step 2: Assume that the statement is true for some natural number k . That is k ( k + 1 ) ( k + 2 ) is divisible by 6 -----(2) Step 3: Prove that the statement is true for the next natural number k + 1 ...

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Chapter 12.4, Problem 22AYU

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To prove: The given statement $n (n + 1) (n + 2)$ is divisible by 6 is true for all natural numbers $n$ using the Principle of Mathematical Induction.

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Chapter 12.4, Problem 21AYU

Chapter 12.4, Problem 23AYU

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To prove: The given statement n ( n + 1 ) ( n + 2 ) is divisible by 6 is true for all natural numbers n using the Principle of Mathematical Induction.

Solution Summary: The author explains the Principle of Mathematical Induction. The statement is true for the natural number n.

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To prove: The given statement $n (n + 1) (n + 2)$ is divisible by 6 is true for all natural numbers $n$ 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 ( n + 1 ) ( n + 2 ) is divisible by 6 is true for all natural numbers n using the Principle of Mathematical Induction.

Solution Summary: The author explains the Principle of Mathematical Induction. The statement is true for the natural number n.

Videos

To prove: The given statement n(n + 1)(n + 2) is divisible by 6 is true for all natural numbers n using the Principle of Mathematical Induction.

Want to see the full answer?

Chapter 12 Solutions

Additional Math Textbook Solutions

To prove: The given statement $n (n + 1) (n + 2)$ is divisible by 6 is true for all natural numbers $n$ using the Principle of Mathematical Induction.