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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.
Ans: Our experts will give the answer soon.
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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.
Describe the sample space for the indicated experiment: A coin is tossed and then a die is rolled only in case a head is shown on the coin.
Find the sum of all numbers between 200 and 400 which are divisible by 7.
The sum of first three terms of a G.P. is and their product is 1. Find the common ratio and the terms.
If is the A.M. between a and b, then find the value of n.
The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q2 = ps.
Calculate the mean deviation about median age for the age distribution of 100 persons given below:
Age 16-20 21-25 26-30 31-35 36-40 41-45 46-50 51-55
Number 5 6 12 14 26 12 16 9
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an arithmetic progression. Find the numbers.
Find the sum of the products of the corresponding terms of the sequences 2, 4, 8, 16, 32 and 128, 32, 8, 2, .
Describe the sample space for the indicated experiment: A coin is tossed four times.