Mathematical Induction - Questions and Solutions

Question 1
Important
Deleted for CBSE Board 2025 Exams

Question 2 Deleted for CBSE Board 2025 Exams

Question 3 Important Deleted for CBSE Board 2025 Exams

Question 4 Deleted for CBSE Board 2025 Exams

Question 5 Important Deleted for CBSE Board 2025 Exams

Question 6 Deleted for CBSE Board 2025 Exams

Question 7 Important Deleted for CBSE Board 2025 Exams

Question 8 Important Deleted for CBSE Board 2025 Exams

Question 9 Deleted for CBSE Board 2025 Exams

Question 10 Deleted for CBSE Board 2025 Exams

Question 11 Important Deleted for CBSE Board 2025 Exams

Question 12 Deleted for CBSE Board 2025 Exams

Question 13 Important Deleted for CBSE Board 2025 Exams

Question 14 Deleted for CBSE Board 2025 Exams

Question 15 Important Deleted for CBSE Board 2025 Exams

Question 16 Important Deleted for CBSE Board 2025 Exams

Question 17 Important Deleted for CBSE Board 2025 Exams

Question 18 Important Deleted for CBSE Board 2025 Exams

Question 19 Deleted for CBSE Board 2025 Exams

Question 20 Deleted for CBSE Board 2025 Exams

Question 21 Important Deleted for CBSE Board 2025 Exams

Question 22 Deleted for CBSE Board 2025 Exams

Question 23 Important Deleted for CBSE Board 2025 Exams You are here

Question 24 Important Deleted for CBSE Board 2025 Exams

Mathematical Induction

Serial order wise

Last updated at April 16, 2024 by Teachoo

Question23 Prove the following by using the principle of mathematical induction for all n N: 41n 14n is a multiple of 27. Introduction If a number is multiple of 27, then it will come in table of 27 27 1 = 27 27 2 = 54 27 3 = 71 Any number multiple of 27 = 27 Natural number Question23 Prove the following by using the principle of mathematical induction for all n N: 41n 14n is a multiple of 27. Let P(n):41n 14n = 27d , where d N For n=1, L.H.S = 411 141 = 41 14 = 27 = 27 1 = R.H.S P(n) is true for n = 1 Assume P(k) is true 41k 14k = 27m, where m N We will prove that P(k + 1) is true L.H.S = 41k+1 14k+1 = 41k . 411 14k . 141 = 41k . 41 14k . 14 = (27m + 14k) 41 14k . 14 = 41 27m + 41 14k 14k . 14 = 41 27m + 14k (41 14) = 41 27m + 14k (27) = 27 (41m 14k) = 27 r, where r = (41m 14k ) is a natural number 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