Question 14 - Mathematical Induction - Questions and Solutions - Mathematical Induction

Last updated at April 16, 2024 by

Ex 4.1, 14 - Prove (1 + 1/1) (1 + 1/2) (1 + 1/3) .. (1 + 1/n) - Ex 4.1

Ex 4.1, 14 - Chapter 4 Class 11 Mathematical Induction - Part 2
Ex 4.1, 14 - Chapter 4 Class 11 Mathematical Induction - Part 3
Ex 4.1, 14 - Chapter 4 Class 11 Mathematical Induction - Part 4

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Question14 Prove the following by using the principle of mathematical induction for all n ∈ N: ("1 + " 1/1) ("1+" 1/2) ("1+" 1/3)â€Ķ.. ("1+ " 1/𝑛) = (n + 1) Let P(n) : ("1 + " 1/1) ("1+" 1/2) ("1+" 1/3)â€Ķ.. ("1+ " 1/𝑛) = (n + 1) For n = 1, L.H.S = ("1 + " 1/1) = 1 + 1 = 2 R.H.S = (1 + 1) = 2 Thus, L.H.S. = R.H.S , âˆīP(n) is true for n = 1 Assuming P(k) is true P(k) : ("1 + " 1/1) ("1+" 1/2) ("1+" 1/3)â€Ķ.. ("1+ " 1/𝑘) = (k + 1) We will prove P(k + 1) is true R.H.S = ((k + 1) + 1) L.H.S = ("1 + " 1/1) ("1+" 1/2) ("1+" 1/3)â€Ķ.. ("1+ " 1/((k +1) )) âˆī By the principle of mathematical induction, P(n) is true for n, where n is a natural number

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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 and Computer Science at Teachoo