Example 8 - Prove rule of exponents (ab)n = anbn - Equal - Multiplication

Example 8 - Chapter 4 Class 11 Mathematical Induction - Part 2
Example 8 - Chapter 4 Class 11 Mathematical Induction - Part 3

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Example 8 Prove the rule of exponents (ab)n = anbn by using principle of mathematical induction for every natural number. Let P(n) : (ab)n = anbn. For n = 1 , L.H.S = (ab)1 = ab R.H.S = a1b1 = a b = ab Thus, L.H.S. = R.H.S , P(n) is true for n = 1 Assuming P(k) is true P(k) : (ab)k = ak bk We will prove that P(k + 1) is true. R.H.S = ak+1 bk+1 L.H.S = (ab)k+1 By the principle of mathematical induction, P(n) is true for n, where n is a natural number

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.