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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.
Chapter 4 Principle of Mathemetical Induction
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.
Download pdf of NCERT Solutions for Class Mathematics Chapter 4 Principle of Mathemetical Induction
Exercise 1
Popular Questions of Class 11 Mathematics
- Q:-
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
- Q:-
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
- Q:-
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
- Q:- Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
- Q:-
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.
- Q:-
How many terms of G.P. 3, 32, 33, … are needed to give the sum 120?
- Q:-
Find the sum of all numbers between 200 and 400 which are divisible by 7.
- Q:- Write the following sets in roster form:
(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.
- Q:-
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
Recently Viewed Questions of Class 11 Mathematics
- Q:-
The 4th term of a G.P. is square of its second term, and the first term is –3. Determine its 7th term.
- Q:-
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.
- Q:-
If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are
. - Q:-
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
- Q:-
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
- Q:-
Given a G.P. with a = 729 and 7th term 64, determine S7.
- Q:-
Find the sum of all numbers between 200 and 400 which are divisible by 7.
- Q:- Find the sum to n terms of the A.P., whose kth term is 5k + 1.
- Q:- Write the first five terms of the sequences whose nth term is \begin{align} a_n = \frac {n}{n+1}\end{align}
- Q:-
Describe the sample space for the indicated experiment: A coin is tossed and a die is thrown.
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