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4. Principle of Mathematical Induction-Introduction Mathematics Class 11 In English-CBSE Notes
Last Updated : 12 March 2026
Get updated Maths Concepts for mathematics for class 11 chapter 4. Principle of Mathematical Induction Topic Introduction with clear explanations free access in English medium.
4. Principle of Mathematical Induction-Introduction Mathematics Class 11 In English-CBSE Notes
Last Updated : 12 March 2026
4. Principle of Mathematical Induction-Introduction Mathematics Class 11 In English-CBSE Notes
4. Principle of Mathematical Induction
Introduction
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)
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NCERT Solutions for Class 11 mathematics Chapter 4. Principle of Mathematical Induction Topic Introduction
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About Chapter 4. Principle of Mathematical Induction of Class 11 mathematics
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4. Principle of Mathematical Induction-Introduction Mathematics Class 11 In English-CBSE Notes
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