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Get CBSE Notes for Class 11 Mathematics Chapter 4. Principle of Mathematical Induction: Introduction prepared by experts as per the latest NCERT syllabus and CBSE exam pattern. These concise and easy-to-understand notes cover important definitions, formulas, diagrams, and key concepts from the chapter to help students in quick revision and effective exam preparation. Whether you are studying for school tests, board exams, or competitive exams, these notes provide a reliable study resource. Designed in simple language with point-wise explanations, they save time and enhance learning efficiency. Download free PDF notes, explore solved examples, and strengthen your understanding of [Topic Name] for scoring high marks. Perfect for Class 11 students who want clear, structured, and exam-oriented notes for CBSE Mathematics.
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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Ace your exams with CBSE Notes for Class 11 Mathematics chapter 4. Principle of Mathematical Induction: Introduction . These notes provide a clear explanation of important concepts, formulas, diagrams, and solved examples from the NCERT syllabus. Specially designed for Class 11 students, the notes are structured in a simple, point-wise manner to make revision quick and effective. Whether you are preparing for school tests, board exams, or competitive exams, these Mathematics notes will boost your confidence and save valuable study time. You can also download Mathematics class 11 chapter 4. Principle of Mathematical Induction free PDF notes for offline learning. With easy-to-grasp language, exam tips, and well-organized content, these CBSE Mathematics notes on chapter 4. Principle of Mathematical Induction – Introduction are the perfect study companion for scoring high marks and mastering the subject.
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