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Class 11 Maths NCERT Solutions For Chapter 4 Principle of Mathematical Induction

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Chapter 4 Principle of Mathematical Induction

Download NCERT Solutions for Class 11 Mathematics

(Link of Pdf file is given below at the end of the Questions List)

In this pdf file you can see answers of following Questions

EXERCISE 4.1

Prove the following by using the principle of mathematical induction for all n ∈ N:


Question 1. 1 + 3 + 32 + ... + 3n – 1 = (3 1) 2 n − .


Question 2. 13 + 23 + 33 + … +n3 = 2 ( 1) 2 n n + .


Question 3. 1 1 1 1 2 (1 2) (1 2 3) (1 2 3 ) ( 1) ... n ...n n + + + + = + + + + + + + .


Question 4. 1.2.3 + 2.3.4 +…+ n(n+1) (n+2) = ( 1)( 2)( 3) 4 n n + n + n + .


Question 5. 1.3 + 2.32 + 3.33 +…+ n.3n = (2 1)3 1 3 4 n − n+ + .


Question 6. 1.2 + 2.3 + 3.4 +…+ n.(n+1) = ( 1)( 2) 3 n n + n +.


Question 7. 1.3 + 3.5 + 57 +…+ (2n–1) (2n+1) = (4 2 6 1) 3 n n + n − .


Question 8. 1.2 + 2.22 + 3.22 + ...+n.2n = (n–1) 2n + 1 + 2.


Question 9. 1 1 1 ... 1 1 1 2 4 8 2n 2n + + + + = − .


Question 10. 1 1 1 ... 1 2.5 5.8 8.11 (3 1)(3 2) (6 4) n n n n + + + + = − + + .


Question 11. 1 1 1 ... 1 ( 3) 1.2.3 2.3.4 3.4.5 ( 1)( 2) 4( 1)( 2)


Question 12. a + ar + ar2 +…+ arn-1 = ( 1) 1 a rn r − − .


Question 13. 2 2 1 3 1 5 1 7 ... 1 (2 1) ( 1) 1 4 9 n n


Question 14. 12 + 32 + 52 + …+ (2n–1)2 = (2 1)(2 1) 3 n n − n + .


Question 15. 1 1 1 ... 1 1.4 4.7 7.10 (3 2)(3 1) (3 1) n n n n + + + + = − + + .


Question 16. 1 1 1 ... 1 3.5 5.7 7.9 (2 1)(2 3) 3(2 3) n n n n + + + + = + + + .


Question 17. 1 + 2 + 3 +…+ n < 1 8 (2n + 1)2.


Question 18. n (n + 1) (n + 5) is a multiple of 3.


Question 19. 102n – 1 + 1 is divisible by 11.


Question 20. x2n – y2n is divisible by x + y.


Question 21. 32n+2 – 8n – 9 is divisible by 8.


Question 22. 41n – 14n is a multiple of 27.


Question 23."> (2n + 7) < (n + 3)2.

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