Read and download NCERT Class 11 Maths Principle Of Mathematical Induction Questions in NCERT book for Class 11 Mathematics. You can download latest NCERT eBooks chapter wise in PDF format free from Studiestoday.com. This Mathematics textbook for Class 11 is designed by NCERT and is very useful for students. Please also refer to the NCERT solutions for Class 11 Mathematics to understand the answers of the exercise questions given at the end of this chapter
NCERT Book for Class 11 Mathematics Chapter 4 Principle of Mathematical Induction
Class 11 Mathematics students should refer to the following NCERT Book Chapter 4 Principle of Mathematical Induction in Class 11. This NCERT Book for Class 11 Mathematics will be very useful for exams and help you to score good marks
Chapter 4 Principle of Mathematical Induction NCERT Book Class 11
4.1 Overview Mathematical induction is one of the techniques which can be used to prove variety of mathematical statements which are formulated in terms of n, where n is a positive integer.
4.1.1 The principle of mathematical induction Let P(n) be a given statement involving the natural number n such that
(i) The statement is true for n = 1, i.e., P(1) is true (or true for any fixed natural number) and
(ii) If the statement is true for n = k (where k is a particular but arbitrary natural number), then the statement is also true for n = k + 1, i.e, truth of P(k) implies the truth of P(k + 1). Then P(n) is true for all natural numbers n.
4.2 Solved Examples
Short Answer Type Prove statements in Examples 1 to 5, by using the Principle of Mathematical Induction for all n ∈ N, that :
Example 1 1 + 3 + 5 + ... + (2n – 1) = n2
Solution Let the given statement P(n) be defined as P(n) : 1 + 3 + 5 +...+ (2n – 1) = n2, for n ∈ N. Note that P(1) is true, since
P(1) : 1 = 12
Assume that P(k) is true for some k ∈ N, i.e., P(k) : 1 + 3 + 5 + ... + (2k – 1) = k 2 Now, to prove that P(k + 1) is true, we have
1 + 3 + 5 + ... + (2k – 1) + (2k + 1)
= k2 + (2k + 1) (Why?)
= k2 + 2k + 1 = (k + 1)2
Please refer to attached file for NCERT Class 11 Maths Principle Of Mathematical Induction Questions
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| NCERT Class 11 Maths Relations And Functions Questions |
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| NCERT Class 11 Maths Trigonometric Functions Questions |
| NCERT Class 11 Maths Principle Of Mathematical Induction |
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| NCERT Class 11 Maths Limits And Derivatives Questions |
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| NCERT Class 11 Maths Mathematical Reasoning Questions |
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| NCERT Class 11 Maths Statistics Questions |
| NCERT Class 11 Maths Probability |
| NCERT Class 11 Maths Probability Questions |
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Mathematics NCERT Book Class 11 Chapter 4 Principle of Mathematical Induction
The above NCERT Books for Class 11 Mathematics Chapter 4 Principle of Mathematical Induction have been published by NCERT for latest academic session. The textbook by NCERT for Chapter 4 Principle of Mathematical Induction Mathematics Class 11 is being used by various schools and almost all education boards in India. Teachers have always recommended students to refer to Chapter 4 Principle of Mathematical Induction NCERT etextbooks as the exams for Class 11 Mathematics are always asked as per the syllabus defined in these ebooks. These Class 11 Chapter 4 Principle of Mathematical Induction book for Mathematics also includes collection of question. We have also provided NCERT solutions for Class 11 Mathematics which have been developed by teachers of StudiesToday.com after thorough review of the latest book and based on pattern of questions in upcoming exams for Class 11 students.
NCERT Book Class 11 Mathematics Chapter 4 Principle of Mathematical Induction
The latest NCERT book for Chapter 4 Principle of Mathematical Induction pdf have been published by NCERT based on the latest research done for each topic which has to be taught to students in all classes. The books for Class 11 Mathematics Chapter 4 Principle of Mathematical Induction are designed to enhance the overall understanding of students. All Class 11 NCERT textbooks have been written in an easy to understand language which will help to enhance the overall level of Class 11 students.
Chapter 4 Principle of Mathematical Induction NCERT Book Class 11 Mathematics
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Class 11 Mathematics Chapter 4 Principle of Mathematical Induction NCERT Book
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Class 11 Chapter 4 Principle of Mathematical Induction NCERT Book Mathematics
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