#### 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

## Chapter 4: Principle of Mathematical Induction

### NCERT solutions for Class 11 Mathematics 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}

## Chapter 4: Principle of Mathematical Induction

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

NCERT solutions for Class 11 Mathematics chapter 4 (Principle of Mathematical Induction) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 11 Mathematics solutions in a manner that help students grasp basic concepts better and faster.

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

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

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