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

Mathematical Induction - Questions and Solutions

Question 1
Important
Deleted for CBSE Board 2024 Exams

Question 2 Deleted for CBSE Board 2024 Exams

Question 3 Important Deleted for CBSE Board 2024 Exams

Question 4 Deleted for CBSE Board 2024 Exams

Question 5 Important Deleted for CBSE Board 2024 Exams

Question 6 Deleted for CBSE Board 2024 Exams

Question 7 Important Deleted for CBSE Board 2024 Exams

Question 8 Important Deleted for CBSE Board 2024 Exams

Question 9 Deleted for CBSE Board 2024 Exams

Question 10 Deleted for CBSE Board 2024 Exams

Question 11 Important Deleted for CBSE Board 2024 Exams

Question 12 Deleted for CBSE Board 2024 Exams

Question 13 Important Deleted for CBSE Board 2024 Exams

Question 14 Deleted for CBSE Board 2024 Exams

Question 15 Important Deleted for CBSE Board 2024 Exams

Question 16 Important Deleted for CBSE Board 2024 Exams

Question 17 Important Deleted for CBSE Board 2024 Exams

Question 18 Important Deleted for CBSE Board 2024 Exams

Question 19 Deleted for CBSE Board 2024 Exams

Question 20 Deleted for CBSE Board 2024 Exams

Question 21 Important Deleted for CBSE Board 2024 Exams

Question 22 Deleted for CBSE Board 2024 Exams

Question 23 Important Deleted for CBSE Board 2024 Exams

Question 24 Important Deleted for CBSE Board 2024 Exams You are here

Mathematical Induction

Serial order wise

Last updated at May 29, 2023 by Teachoo

Question24 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 Question24 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