Last updated at Feb. 15, 2020 by Teachoo

Transcript

Ex 4.1,24 Prove the following by using the principle of mathematical induction for all n, n is a natural number (2n +7) < (n + 3)2 Introduction Since 1 < 100 then 1 < 100 + 5 i.e. 1 < 105 We will use this theory in our question Ex 4.1,24 Prove the following by using the principle of mathematical induction for all n, n is a natural number (2n +7) < (n + 3)2 Let P(n): (2n +7) < (n + 3)2 For n = 1 L.H.S = (2.1 + 7) = 2 + 7 = 9 R.H.S = (1 + 3)2 = 16 Since 9 < 16 L.H.S < R.H.S P(n) is true for n = 1 Assume P(k) is true (2k + 7) < (k + 3)2 We will prove that P(k + 1) is true. R.H.S = ((k+1) + 3)2 L.H.S = (2(k+1) + 7) L.H.S < R.H.S P(k + 1) is true whenever P(k) is true. By the principle of mathematical induction, P(n) is true for n, where n is a natural number

Ex 4.1

Ex 4.1, 1
Important
Deleted for CBSE Board 2022 Exams

Ex 4.1, 2 Deleted for CBSE Board 2022 Exams

Ex 4.1, 3 Important Deleted for CBSE Board 2022 Exams

Ex 4.1, 4 Deleted for CBSE Board 2022 Exams

Ex 4.1, 5 Important Deleted for CBSE Board 2022 Exams

Ex 4.1, 6 Deleted for CBSE Board 2022 Exams

Ex 4.1, 7 Important Deleted for CBSE Board 2022 Exams

Ex 4.1, 8 Important Deleted for CBSE Board 2022 Exams

Ex 4.1, 9 Deleted for CBSE Board 2022 Exams

Ex 4.1, 10 Deleted for CBSE Board 2022 Exams

Ex 4.1, 11 Important Deleted for CBSE Board 2022 Exams

Ex 4.1, 12 Deleted for CBSE Board 2022 Exams

Ex 4.1, 13 Important Deleted for CBSE Board 2022 Exams

Ex 4.1, 14 Deleted for CBSE Board 2022 Exams

Ex 4.1, 15 Important Deleted for CBSE Board 2022 Exams

Ex 4.1, 16 Important Deleted for CBSE Board 2022 Exams

Ex 4.1, 17 Important Deleted for CBSE Board 2022 Exams

Ex 4.1, 18 Important Deleted for CBSE Board 2022 Exams

Ex 4.1, 19 Deleted for CBSE Board 2022 Exams

Ex 4.1, 20 Deleted for CBSE Board 2022 Exams

Ex 4.1, 21 Important Deleted for CBSE Board 2022 Exams

Ex 4.1, 22 Deleted for CBSE Board 2022 Exams

Ex 4.1, 23 Important Deleted for CBSE Board 2022 Exams

Ex 4.1, 24 Important Deleted for CBSE Board 2022 Exams You are here

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.