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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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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.

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.

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.

**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 ).

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