Question 18 - Inequality - Mathematical Induction

Last updated at Dec. 16, 2024 by

Ex 4.1, 18 - Prove 1 + 2 + 3 + .. + n < 1/8 (2n+1)2 - Induction - Inequality

Ex 4.1, 18 - Chapter 4 Class 11 Mathematical Induction - Part 2
Ex 4.1, 18 - Chapter 4 Class 11 Mathematical Induction - Part 3

Go Ad-free

Transcript

Question18 Prove the following by using the principle of mathematical induction for all n N: 1 + 2 + 3 + ..+ n < 1/8 (2n+1)2 Let P (n) : 1 + 2 + 3 + ..+ n < 1/8 (2n+1)2 For n = 1 L.H.S = 1 R.H.S = 1/8 (2.1 + 1)2 = 1/8 ( 2 + 1)2 = 1/8 (3)2 = 9/8 Since 1 < 9/8 Thus L.H.S < R.H.S P(n) is true for n = 1 Assume P(k) is true 1 + 2 + 3 + ..+ k < 1/8 (2k+1)2 We will prove that P(k + 1) is true. L.H.S = 1 + 2 + 3 + . + (k + 1) R.H.S = 1/8 (2(k + 1) + 1)2

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