NCERT solutions for Mathematics Class 11 chapter 4 - Principle of Mathematical Induction [Latest edition]

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Solutions for Chapter 4: Principle of Mathematical Induction

Below listed, you can find solutions for Chapter 4 of CBSE, Karnataka Board PUC NCERT for Mathematics Class 11.


Exercise 4.1
Exercise 4.1 [Pages 94 - 95]

NCERT solutions for Mathematics Class 11 Chapter 4 Principle of Mathematical Induction Exercise 4.1 [Pages 94 - 95]

Exercise 4.1 | Q 1 | Page 94

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

`1 + 3 + 3^2 + ... + 3^(n – 1) =((3^n -1))/2`

Exercise 4.1 | Q 2 | Page 94

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

`1^3 +  2^3 + 3^3 + ... + n^3 = ((n(n+1))/2)^2`

Exercise 4.1 | Q 3 | Page 94

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

`1+ 1/((1+2)) + 1/((1+2+3)) +...+ 1/((1+2+3+...n)) = (2n)/(n +1)`
Exercise 4.1 | Q 4 | Page 94

Prove the following by using the principle of mathematical induction for all n ∈ N: 1.2.3 + 2.3.4 + … + n(n + 1) (n + 2)  = `(n(n+1)(n+2)(n+3))/(4(n+3))`

Exercise 4.1 | Q 5 | Page 94

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

1.3 + 2.3^3 + 3.3^3  +...+ n.3^n = `((2n -1)3^(n+1) + 3)/4`
Exercise 4.1 | Q 6 | Page 94

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

1.2 + 2.3 + 3.4+ ... + n(n+1) = `[(n(n+1)(n+2))/3]`

Exercise 4.1 | Q 7 | Page 94

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

1.3 + 3.5 + 5.7 + ...+(2n -1)(2n + 1) = `(n(4n^2 + 6n -1))/3`
Exercise 4.1 | Q 8 | Page 94

Prove the following by using the principle of mathematical induction for all n ∈ N: 1.2 + 2.22 + 3.22 + … + n.2n = (n – 1) 2n+1 + 2

Exercise 4.1 | Q 9 | Page 94

Prove the following by using the principle of mathematical induction for all n ∈ N: `1/2 + 1/4 + 1/8 + ... + 1/2^n = 1 - 1/2^n`

 
Exercise 4.1 | Q 10 | Page 94

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

`1/2.5 + 1/5.8 + 1/8.11 + ... + 1/((3n - 1)(3n + 2)) = n/(6n + 4)`
Exercise 4.1 | Q 11 | Page 94

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

1/1.2.3 + 1/2.3.4 + 1/3.4.5 + ...+ `1/(n(n+1)(n+2)) = (n(n+3))/(4(n+1) (n+2))`
Exercise 4.1 | Q 12 | Page 95

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

`a + ar + ar^2 + ... + ar^(n -1) = (a(r^n - 1))/(r -1)`
Exercise 4.1 | Q 13 | Page 95

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

(1+3/1)(1+ 5/4)(1+7/9)...`(1 + ((2n + 1))/n^2) = (n + 1)^2`

 
Exercise 4.1 | Q 14 | Page 95

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

`(1+ 1/1)(1+ 1/2)(1+ 1/3)...(1+ 1/n) = (n + 1)`

Exercise 4.1 | Q 15 | Page 95

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

`1^2 + 3^2 + 5^2 + ... + (2n -1)^2 = (n(2n - 1) (2n + 1))/3`
Exercise 4.1 | Q 16 | Page 95

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

`1/1.4 + 1/4.7 + 1/7.10 + ... + 1/((3n - 2)(3n + 1)) = n/((3n + 1))`

Exercise 4.1 | Q 17 | Page 95

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

`1/3.5 + 1/5.7 + 1/7.9 + ...+ 1/((2n + 1)(2n +3)) = n/(3(2n +3))`
Exercise 4.1 | Q 18 | Page 95

Prove the following by using the principle of mathematical induction for all n ∈ N: `1+2+ 3+...+n<1/8(2n +1)^2`

Exercise 4.1 | Q 19 | Page 95

Prove the following by using the principle of mathematical induction for all n ∈ Nn (n + 1) (n + 5) is a multiple of 3.

Exercise 4.1 | Q 20 | Page 95

Prove the following by using the principle of mathematical induction for all n ∈ N: 102n – 1 + 1 is divisible by 11

Exercise 4.1 | Q 21 | Page 95

Prove the following by using the principle of mathematical induction for all n ∈ Nx2n – y2n is divisible by x y.

Exercise 4.1 | Q 22 | Page 95

Prove the following by using the principle of mathematical induction for all n ∈ N: 32n + 2 – 8n– 9 is divisible by 8.

Exercise 4.1 | Q 23 | Page 95

Prove the following by using the principle of mathematical induction for all n ∈ N: 41n – 14n is a multiple of 27.

Exercise 4.1 | Q 24 | Page 95

Prove the following by using the principle of mathematical induction for all n ∈ N (2+7) < (n + 3)2

Solutions for Chapter 4: Principle of Mathematical Induction

Exercise 4.1

NCERT solutions for Mathematics Class 11 chapter 4 - Principle of Mathematical Induction

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Concepts covered in Mathematics Class 11 chapter 4 Principle of Mathematical Induction are Motivation, Principle of Mathematical Induction.

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Get the free view of Chapter 4, Principle of Mathematical Induction Mathematics Class 11 additional questions for Mathematics Mathematics Class 11 CBSE, Karnataka Board PUC, and you can use Shaalaa.com to keep it handy for your exam preparation.

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