Check sibling questions

Example 8 - Mathematical Induction

Last updated at May 29, 2023 by

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

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

Book a free demo

Transcript

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

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.