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Q19 Prove the following by using the principle of mathematical induction for all n ∈ N:
n (n + 1) (n + 5) is a multiple of 3.
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Principle of Mathemetical Induction Question Answers: NCERT Class 11 Mathematics
Welcome to the Chapter 4 - Principle of Mathemetical Induction, Class 11 Mathematics - NCERT Solutions page. Here, we provide detailed question answers for Chapter 4 - Principle of Mathemetical Induction.The page is designed to help students gain a thorough understanding of the concepts related to natural resources, their classification, and sustainable development.
Our solutions explain each answer in a simple and comprehensive way, making it easier for students to grasp key topics and excel in their exams. By going through these Principle of Mathemetical Induction question answers, you can strengthen your foundation and improve your performance in Class 11 Mathematics. Whether you're revising or preparing for tests, this chapter-wise guide will serve as an invaluable resource.
This chapter is all about proving the given statement is true or not by the process of induction. We deal with natural numbers because it is the least inductive subset of real numbers. Least inductive means it has the least fixed point for an operation definable by a positive formula for some natural number n. In this chapter, we will discuss the principle of mathematical induction and its simple applications.
Exercise 1
Key Features of NCERT Class 11 Mathematics Chapter 'Principle of Mathemetical Induction' question answers :
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Popular Questions of Class 11 Mathematics
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Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
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A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
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(i) A = {x: x is an integer and - 3 < x < 7}.
(ii) B = {x: x is a natural number less than 6}.
(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}
(iv) D = {x: x is a prime number which is divisor of 60}.
(v) E = The set of all letters in the word TRIGONOMETRY.
(vi) F = The set of all letters in the word BETTER. - Q:-
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
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Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
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Show that the sum of (m + n)th and (m – n)th terms of an A.P. is equal to twice the mth term.
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An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.
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Given a G.P. with a = 729 and 7th term 64, determine S7.
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