Open App

Mathematics Exam > Mathematics Videos > Mathematics for Competitive Exams > Monotonic Sequence & Eventually Monotonic Sequence

Monotonic Sequence & Eventually Monotonic Sequence Video Lecture | Mathematics for Competitive Exams

Q: 4. What are the properties of a monotonic sequence?

Ans. A monotonic sequence has the following properties:- If the sequence is non-decreasing, it means that each term is greater than or equal to the previous term.- If the sequence is non-increasing, it means that each term is less than or equal to the previous term.- A monotonic sequence can have a limit or can diverge to positive or negative infinity.

	Mathematics for Competitive Exams 98 videos\|27 docs\|30 tests

Mathematics for Competitive Exams

98 videos|27 docs|30 tests

Join Course for Free

FAQs on Monotonic Sequence & Eventually Monotonic Sequence Video Lecture - Mathematics for Competitive Exams

1. What is a monotonic sequence?

Ans. A monotonic sequence is a sequence of numbers that either increases or decreases consistently as we move along the sequence. In other words, it is a sequence that is either entirely non-increasing or non-decreasing.

2. What is an eventually monotonic sequence?

Ans. An eventually monotonic sequence is a sequence that may not be monotonic initially, but becomes monotonic after a certain point in the sequence. This means that there exists a term in the sequence beyond which all the terms are either non-increasing or non-decreasing.

3. How can we determine if a sequence is monotonic?

Ans. To determine if a sequence is monotonic, we can observe the signs of the differences between consecutive terms. If the differences are always non-negative or always non-positive, then the sequence is monotonic. If the differences have both positive and negative values, then the sequence is not monotonic.

4. What are the properties of a monotonic sequence?

Ans. A monotonic sequence has the following properties: - If the sequence is non-decreasing, it means that each term is greater than or equal to the previous term. - If the sequence is non-increasing, it means that each term is less than or equal to the previous term. - A monotonic sequence can have a limit or can diverge to positive or negative infinity.

5. How can we determine if a sequence is eventually monotonic?

Ans. To determine if a sequence is eventually monotonic, we can check if there exists a term in the sequence beyond which all the terms have the same sign in their differences. If such a term exists, then the sequence is eventually monotonic. If the terms do not have the same sign in their differences, then the sequence is not eventually monotonic.

Related Exams

IIT JAM

About this Video

	1.5K Views
	4.89/5 Rating
	Nov 24, 2024 Last updated

Video Description: Monotonic Sequence & Eventually Monotonic Sequence for Mathematics 2024 is part of Mathematics for Competitive Exams preparation. The notes and questions for Monotonic Sequence & Eventually Monotonic Sequence have been prepared according to the Mathematics exam syllabus. Information about Monotonic Sequence & Eventually Monotonic Sequence covers all important topics for Mathematics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Monotonic Sequence & Eventually Monotonic Sequence.

Introduction of Monotonic Sequence & Eventually Monotonic Sequence in English is available as part of our Mathematics for Competitive Exams for Mathematics & Monotonic Sequence & Eventually Monotonic Sequence in Hindi for Mathematics for Competitive Exams course. Download more important topics related with notes, lectures and mock test series for Mathematics Exam by signing up for free.

Description

Video Lecture & Questions for Monotonic Sequence & Eventually Monotonic Sequence Video Lecture | Mathematics for Competitive Exams - Mathematics full syllabus preparation | Free video for Mathematics exam to prepare for Mathematics for Competitive Exams.

Information about Monotonic Sequence & Eventually Monotonic Sequence

Here you can find the meaning of Monotonic Sequence & Eventually Monotonic Sequence defined & explained in the simplest way possible. Besides explaining types of Monotonic Sequence & Eventually Monotonic Sequence theory, EduRev gives you an ample number of questions to practice Monotonic Sequence & Eventually Monotonic Sequence tests, examples and also practice Mathematics tests.

	Mathematics for Competitive Exams 98 videos\|27 docs\|30 tests

Mathematics for Competitive Exams

98 videos|27 docs|30 tests

Join Course for Free

Explore Courses for Mathematics exam

Signup for Free!

Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.

Start learning for Free

10M+ students study on EduRev