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 Book Class 11 Mathematics 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. Along with Mathematics Class 11 NCERT Book in Pdf for Chapter 4 Principle of Mathematical Induction we have provided all NCERT Books in English Medium for Class 11 which will be really helpful for students who have opted for english language as a medium. Class 11 students will need their books in English so we have provided them here for all subjects in Class 11.
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