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Ncert Solution | Ncert Solution for class 11th | Ncert Solution for 11 Maths | NCERT MATHS CHAPTER 4 PRINCIPLE OF MATHEMATICAL INDUCTION
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NCERT Solutions for class 11 maths Chapter 4 PRINCIPLE OF MATHEMATICAL INDUCTION

Ncert Solutions for class 11 maths Chapter 4 PRINCIPLE OF MATHEMATICAL INDUCTION  is prepared by CBSE STUDENT eCARE Expert to score good marks in class 11. Class 11 maths chapter 4 PRINCIPLE OF MATHEMATICAL INDUCTION contains many topics which are very important to score good in class 11. There are some important topics of Chapter 4 PRINCIPLE OF MATHEMATICAL INDUCTION is mentioned below:

his 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 include-
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).



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Some Questions are asked by class 11 Students related to Chapter 4 PRINCIPLE OF MATHEMATICAL INDUCTION

What are the principles of mathematical induction?

 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., truth of P(k) implies the truth of P (k + 1). Then, P(n) is true for all natural numbers n. Property (i) is simply a statement of fact.

What is the first principle of mathematical induction?

The principle of mathematical induction is then: If the integer 0 belongs to the class F and F is hereditary, every nonnegative integer belongs to F. Alternatively, if the integer 1 belongs to the class F and F is hereditary, then every positive integer belongs to F.

What is the induction formula?

Mathematical Induction is a technique of proving a statement, theorem or formula which is thought to be true, for each and every natural number n. +n3 = (n(n+1) / 2)2, the statement is considered here as true for all the values of natural numbers.

What is the importance of mathematical induction?

Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true for all natural numbers (non-negative integers ).

What are the limitations of mathematical induction?

One major limitation of mathematical Induction is that it is limited to items quantifiable in the set of numbers.