Our CBSE Notes for Introduction Class 11 maths 4. Principle of Mathematical Induction - CBSE Notes - Toppers Study is the best material for English Medium students cbse board and other state boards students.

# Introduction Class 11 maths 4. Principle of Mathematical Induction - CBSE Notes - Toppers Study

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## Introduction Class 11 maths 4. Principle of Mathematical Induction - CBSE Notes - Toppers Study

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### Introduction class 11 Mathematics Chapter 4. Principle of Mathematical Induction

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- Introduction Class 11 Maths 4. Principle Of Mathematical Induction - CBSE Notes - Toppers Study
- Class 11 Ncert Solutions
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## 4. Principle of Mathematical Induction

### | Introduction |

## Introduction Class 11 maths 4. Principle of Mathematical Induction - CBSE Notes - Toppers Study

**4. Principle of Mathematical Induction**

Mathematical induction is a technique for proving a statement, theorem, or a formula, that is asserted about every natural number.

The word induction means the generalisation from particular cases or facts.

**Statement:** A sentence which can be judged to be true or false is called statement.

**Mathematical example: **

(i) Eight is divisible by two.

(ii) Any number divisible by two is an even number,

therefore,

(iii) Eight is an even number.

Here statements (i) and (ii) are true, so

using (i) and (ii)

(iii) is also true

**Deduction:** Deduction is a process in which a statement is given to be proven, often called a conjecture or a theorem in mathematics. deduction is the application of a general case to a particular case.

The Principle of Mathematical induction:

Concept:

(i) If a statement is true for one event then statement will be true for all given events.

This is the underlying principle of mathematical induction.

Steps:

Suppose there is a given statement P(n) involving the natural number ** n** such that:

**Step I: **

First prove for P(1) where n =1 and n ∈ N;

When P(1) is true

then

**Step II **

Assume that P(k) is true for some positive integer k,

And replace n by k and make that a equation (I)

**Step III **

Then Add a extra term e.i (k +1) in equation I and replace n by (k + 1) from formula.

Then prove for (k + 1)

##### Other Pages of this Chapter: 4. Principle of Mathematical Induction

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