NCERT Solutions for Class 11 Maths Chapter 4 – Principle of Mathematical Induction
NCERT Solutions for Class 11 Maths Chapter 4 provided by maths experts at Instasolv will solve all your doubts related to Mathematical Induction. The solutions contain a very easy description of all the questions so that you can master the topics of the chapter easily. All our solutions adhere to the latest CBSE exam pattern for class 11 maths so that you can prepare for your exams without any trouble.
Chapter 4 NCERT Solutions for Class 11 Maths has a total of 24 questions. All the 24 questions in the exercise require to prove the given mathematical statements through the process of Mathematical Induction. So, lets quickly learn the most important principle on which this entire chapter is based on and let you score highest in your exams.
Important Points for NCERT Solution for Class 11 Maths Chapter 4: Principle of Mathematical Induction
According to CBSE, NCERT Solutions for Class 11 Maths Chapter 4, there are basically two major principles of Mathematical Induction, that include – Deduction and Induction. In the process of Induction, we are provided with statements that signify specific instances, from which we draw conclusions related to generalizations. For example, there are three statements- (i) Samir eats food (ii) Mohan eats food (iii) Samir and Mohan are men, the conclusion will be: All men eat food.
Mathematical Induction is a method of checking the validity of a particular Mathematical statement that is asserted about every natural number. The statements here can be a formula or series, and you will have to prove it with the help of Mathematical Induction.
The chapter first demands us to understand what exactly is a mathematical statement. Let the statement be-
S (n) = 1+2+3+…………+n = n (n+1) 2
Suppose n= 1,
S (1) = 1 = 1 (2) 2 = 1
Thus, L.H.S = R.H.S
The above-given example is a statement. Now we will learn how to prove a particular statement with the help of Mathematical Induction. For that, first, you will require to learn the principles of Mathematical Induction. The principle of the Mathematical Induction says that, if there is a mathematical statement S(n), put 1 in place of n and prove that the statement is true.
The second step is a presumption, let S(n) is true for n=k. And, the final step is that you need to write k+1 is a place of S(n), the result will be S(k+1), and you will have to solve the L.H.S and prove it equal to the R.H.S. If you can do this, then the principle of mathematical induction says that in such a situation, the S(n) statement will be considered true.
Some of the most relevant points related to Chapter 4 of Class 11 Maths NCERT book are:
- Never underestimate the base case, because most of the time, the base case is obvious. Unable to justify the base case can lead to a lot of fallacious proofs.
- Although induction aims to establish the truthfulness of a particular statement, it rarely provides the reasoning behind the problem.
- Revise the earlier chapter on Sets, because it forms an integral part of Mathematical Induction.
- Recheck every step after solving, because a mistake in one step could hamper the final results.
- Since the lesson is related to reasoning, it is essential to relook on the Mathematical Reasoning basics.
- The proof should stand true for all the values consisting of the natural numbers.
- And, always remember proving a given statement is the main motive.
Exercise-wise Discussion on NCERT Solutions for Class 11 Maths Chapter 4
- This chapter has 24 questions that will analyse your understanding level regarding principles of Maths Induction. In all the 24 questions you need to prove whether the given statements are true or not.
- The Solutions provided by Instasolv are according to the pattern of CBSE examination which will help you in preparing for the exams accordingly.
- Our subject experts have solved the questions step by step so as to make them easy to understand.
About NCERT Solution for Class 11 Maths Chapter 4, by Instasolv
The experts at Instasolv don’t ever promote spoon-feeding. We always give you the best of the explanations and want you to solve questions by yourself. This will help you understand the concepts more clearly. For your better understanding, we suggest you read the summary of NCERT Solutions for Class 11 Maths Chapter by Instasolv, again and again, to grasp the Principles of Mathematical Induction more clearly.