Explanation Given: ( a b ) n = a n b n , if ‘ a’ and b are constant. Formula used: According to mathematical induction, if any statement is true for the positive natural numbers like n = k , then it will be true for the statement of n = k + 1 also. So that if the statement P ( k ) is true then, the statement of P ( k + 1 ) is also be true. Proof: If n = 1 , then the statement ( a b ) n = a n b n is: ( a b ) 1 = a 1 b 1 ( a b ) = ( a b ) This statement is correct, so n = 1 is true. Assume that n = k (where k is some positive integers) is true, then the statement ( a b ) n = a n b n is: ( a b ) k = a k b k .... ( 1 ) If statement ( 1 ) i.e., P ( k ) is true, prove that P ( k + 1 ) is also true

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ISBN: 8220100802799

Author: Dugopolski

Publisher: PEARSON

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Chapter 8.7, Problem 45E

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To prove: The statement (ab)n=anbn is true for all each positive integer n.

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Chapter 8.7, Problem 44E

Chapter 8.7, Problem 46E

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To prove: The statement ( a b ) n = a n b n is true for all each positive integer n .

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To prove: The statement (ab)n=anbn is true for all each positive integer n.

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