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

Go Ad-free

Transcript

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

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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo