#### 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

#### 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}