Principle of Mathematical Induction Class 11 Notes - Chapter 4

According to the CBSE Syllabus 2023-24, this chapter has been removed from NCERT Class 11 Maths textbook.

What is Mathematical Induction?

Mathematical induction is a specialized form of working on different cases and coming up with observations. Induction is the compilation of a particular set of facts. This method is used to determine a wide range of statements in which we analyze the legitness of the case. The set should be denumerable in order for mathematical induction to work with an infinite set, meaning that it should have a one-to-one correspondence between the elements of the set in question and the set of positive integers.

In simple terms, this method expresses the set in the form of an implied list of discrete elements such as {1, 2, 3, 4, …}.

Also Refer: Mathematical Induction 

Properties of Mathematical Induction

Mathematical induction has to follow statements with respect to the properties they obey:

• When the value of n is true for statements such as n ≥ 5, we should initiate by satisfying the value n=5, i.e. P(5)
• If the statement provided is true for n=k, and if it satisfies the value n=k, then it will also satisfy n=k+1. In order to prove the trueness of the statement, we have to prove n=k+1.

Inductive Hypothesis

The step mentioned above is the assumption of the trueness of the statement n=k and is referred to as the inductive step or inductive hypothesis.

Let us take an example of the following pattern:

Here we can witness the sum of the first two odd natural numbers is the square of the second number, which is a natural number and the pattern continues.

P(n)=

And P(1) is satisfied, then it is the first step, and the value will satisfy all natural numbers.

Also Read: Principle of Mathematical Induction

Related Links:

• Principle of Mathematical Reasoning
• NCERT Solutions for Class 11 Maths Chapter 4
• NCERT Exemplar for Class 11 Maths Chapter 4
• Understanding Mathematical Induction With Examples