-
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.
Ans: Our experts will give the answer soon.
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.
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. |
Ans: | Our experts will give the answer soon. |
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.
How many terms of G.P. 3, 32, 33, … are needed to give the sum 120?
Find the sum of all numbers between 200 and 400 which are divisible by 7.
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
Give three examples of sentences which are not statements. Give reasons for the answers.
A man starts repaying a loan as first installment of Rs. 100. If he increases the installment by Rs 5 every month, what amount he will pay in the 30th installment?
If a, b, c and d are in G.P. show that
Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that P2Rn = Sn
Using Binomial Theorem, indicate which number is larger (1.1)10000 or 1000.
Find the equation of the circle with centre (0, 2) and radius 2
The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q2 = ps.
If is the A.M. between a and b, then find the value of n.
Find the sum to n terms in the geometric progression
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.