#### Online Mock Tests

#### Chapters

Chapter 2: Relations and Functions

Chapter 3: Trigonometric Functions

▶ Chapter 4: Principle of Mathematical Induction

Chapter 5: Complex Numbers and Quadratic Equations

Chapter 6: Linear Inequalities

Chapter 7: Permutations and Combinations

Chapter 8: Binomial Theorem

Chapter 9: Sequences and Series

Chapter 10: Straight Lines

Chapter 11: Conic Sections

Chapter 12: Introduction to Three Dimensional Geometry

Chapter 13: Limits and Derivatives

Chapter 14: Mathematical Reasoning

Chapter 15: Statistics

Chapter 16: Probability

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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.

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

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`

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`

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

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))`

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

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]`

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

Prove the following by using the principle of mathematical induction for all *n* ∈ *N*: 1.2 + 2.2^{2} + 3.2^{2} + … + *n*.2^{n} = (*n* – 1) 2^{n}^{+1} + 2

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`

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

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

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

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`

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)`

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

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))`

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

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

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

Prove the following by using the principle of mathematical induction for all *n* ∈ *N*: 10^{2}^{n}^{ – 1 }+ 1 is divisible by 11

Prove the following by using the principle of mathematical induction for all *n* ∈ *N*: *x*^{2}^{n} – *y*^{2}^{n} is divisible by* x *+ *y*.

Prove the following by using the principle of mathematical induction for all *n* ∈ *N*: 3^{2}^{n}^{ + 2} – 8*n*– 9 is divisible by 8.

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

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

## Solutions for Chapter 4: Principle of Mathematical Induction

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

Shaalaa.com has the CBSE, Karnataka Board PUC Mathematics Mathematics Class 11 CBSE, Karnataka Board PUC solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. NCERT solutions for Mathematics Mathematics Class 11 CBSE, Karnataka Board PUC 4 (Principle of Mathematical Induction) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.

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

Using NCERT Mathematics Class 11 solutions Principle of Mathematical Induction exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in NCERT Solutions are essential questions that can be asked in the final exam. Maximum CBSE, Karnataka Board PUC Mathematics Class 11 students prefer NCERT Textbook Solutions to score more in exams.

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.