NCERT Solution For Class 11 Maths Chapter 4 - Principle of Mathematical Induction

NCERT Solutions For Class 11 Maths Chapter 4 PDF Free Download

NCERT Solutions For Class 11 Maths Chapter 4 Principle of Mathematical Induction are given in an easy way at BYJU’S. Students learn about the Principle of Mathematical Induction and its application in detail through this chapter. After solving all the questions present in the NCERT textbook and Exemplar, students can easily score maximum marks for the questions of this chapter. 
Principle of Mathematical Induction is a specific technique used to prove certain mathematically accepted statements in algebra and in other applications of Mathematics, such as inductive and deductive reasoning. NCERT Solutions of BYJU’S cover all these concepts and help in scoring full marks for this chapter. These solutions are useful for further studies and for those who are preparing for competitive exams. NCERT Solutions For Class 11 Maths are very accurate and make it easy to crack the exam with good marks.

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NCERT Solutions for Class 11 Maths Chapter 4- Principle of Mathematical Induction

This chapter has only one exercise which will help students in understanding the concepts related to the Principle of Mathematical Induction clearly. The major topic and subtopics covered in Chapter 4  Principle of Mathematical Induction of NCERT Solutions for Class 11 include the following.
4.1 Introduction
Here, students can understand deductive reasoning with suitable examples. This section explains the assumptions that are made on the basis of certain universal facts. 
4.2 Motivation
In this section, mathematical induction is explained with a real-life scenario to make the students understand how it basically works.
4.3 The Principle of Mathematical Induction
This section explains the Principle of Mathematical Induction using inductive step and the inductive hypothesis.
Suppose there is a given statement P(n) involving the natural number n such that

  • The statement is true for n = 1, i.e., P(1) is true
  • If the statement is true for n = k (where k is some positive integer), then the statement is also true for n = k + 1, i.e., the truth of P(k) implies the truth of P (k + 1).

Exercise 4.1 Solutions 24 Questions

Key Features of NCERT Solutions for Class 11 Maths Chapter 4- Principle of Mathematical Induction

Studying the Principle of Mathematical Induction of Class 11 enables the students to understand the process of the proof by induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers. Students also get to know the principle of mathematical induction and its applications after going through the solutions of NCERT questions. The summary of the concepts discussed and used in the solutions of this chapter are:

  1. One key basis for mathematical thinking is deductive reasoning. In contrast to deduction, inductive reasoning depends on working with different cases and developing a conjecture by observing incidences until we have observed each and every case. Thus, in simple language we can say the word ‘induction’ means the generalization from particular cases or facts
  2. The principle of mathematical induction is one such tool which can be used to prove a wide variety of mathematical statements. Each such statement is assumed as P(n) associated with positive integer n, for which the correctness of the case n = 1 is examined. Then assuming the truth of P(k) for some positive integer k, the truth of P (k+1) is established.

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