Calculus - Limits of Sequences

How to Determine the Limit of any kind of Sequences

Created byDániel Csíkos

Last updated 6/2023

English

What you'll learn

How to calculate the limit of any kind of sequences
Squeeze (Sandwich) theorem
Basic notions related to sequences
Orders of magnitude of different type of functions
Limits of fractions
How to determine the index number of convergence
How to deal with square roots
How to deal with cube roots
Definition of Euler's number (e)
How to use Euler's number (e) to determine limits

Course content

8 sections • 28 lectures • 1h 41m total length

Introduction1:39

Definition of sequences2:19
Getting to know the basic notations and the definition of a sequence.
Definition of convergence3:32
Getting to know when the sequence is convergent or divergent. Explanation of the definition of convergence.
Limits of common sequences5:55
All of the important basic limits that you need to calculate the limit of any typical sequence.
Necessary condition of convergence3:34
The necessary condition of convergence and the maining of the notions in it. Monotony, bounded sequences.
Fundamental operations5:06
The operational laws in case of calculating limits of sequences. Addition, difference, product and quotient of sequences.
Practical consequences of the operational laws.
Order of magnitude3:00
The comparison of sequences with infinite limits: the order of maginute of different type of sequences.
Checkpoint - Theoretical introduction to sequences

Limits of fractions - 1. Example4:20
Sample problem of calculating the limits of fractions.
Limits of fractions - 2. Example2:06
Further example of calculating the limits of polynomial fractions.
Limits of fractions - 3. Example3:42
Further example of calculating the limits of polynomial fractions by a slightly different method.
Limits of fractions - 4. Example2:55
Example of calculating the limits of fractions including exponential terms.
Limits of fractions - 5. Example5:04
Example of calculating the limits of fractions including polynomial and exponential terms at the same time.
Checkpoint - Limits of fractions

Searching for index number - 1. Example10:06
Determination of an index number above which the terms of the sequence are within a given distance to the limit of the sequence.
Searching for index number - 2. Example6:49
Determination of an index number above which the terms of the sequence are within a given distance to the limit of the sequence.
Checkpoint - Determination of an index number for a given closeness0:13

Troublesome sequences with square roots - 1. Example4:39
Example of how to deal with square roots with rationalizing in case of challenging sequences.
Troublesome sequences with square roots - 2. Example3:00
Further example of how to deal with square roots in case of challenging sequences.
Troublesome sequences with square roots - 3. Example3:41
Further example of how to deal with square roots in case of challenging sequences.
Troublesome sequences with cube roots - Example5:15
Example of how to deal with cube roots in case of challenging sequences.
Checkpoint - Getting rid of the square roots and cube roots

Limits related to Euler's number (e) - 1. Example3:58
Basic example of determining the limit of a sequence based on the definition of Euler's number.
Limits related to Euler's number (e) - 2. Example4:24
Further, more challenging, example of determining the limit of a sequence related to e (Euler's number).
Limits related to Euler's number (e) - 3. Example3:43
Further, more challenging, example of determining the limit of a sequence related to e (Euler's number).
Checkpoint - Limits based on the definition of Euler's number (e)

Squeeze theorem3:00
The sandwich theorem. Its application to sequences and its special application in case of divergent sequences or sequences with the limit of 0.
Squeeze theorem - 1. Example3:07
Basic example of the application of the squeeze theorem.
Squeeze theorem - 2. Example2:37
Further example of the application of the squeeze theorem.
Squeeze theorem - 3. Example2:41
Advanced example of the application of the squeeze theorem.

Requirements

An average highschool level mathematics knowledge
A desire to get better in mathematics

Description

Welcome!

By completing this course, you are going to be able to determine the limit of any kind of sequence. I'm going to show you the necessary theoretical background in a nutshell. Then I show you lots of practical examples! I believe that you should always learn through solving problems! That's why I made this course practical and I also give you a chance to practice on your own!

I dedicate a separate section to the different kinds of sequences. In every section, I show you how to deal with a basic sequence of that kind, and then I show more and more complicated numerical examples. These sample problems are going to help you understand what you have to do! Finally, there is always a checkpoint at the end of a section to test your knowledge!

I believe in learning through examples so the course is highly practical. If you want to practice even more, you can stop the videos and make an effort of solving the numerical examples by yourself! Or at least you can solve the problems I give you at the checkpoints!

You don't need much of a prior knowledge to take this course. If you know the basic operations and some details about the basic functions, you are good to go! I'm going to clear the necessary details during the lectures, so do not worry about the challenge!

This course is primarily designed for university/college students who are learning Calculus and have to deal with limits of sequences. If you are struggling with this topic, let me help you! Here you are going to get every help that you possibly need! If you have already completed this topic but you feel like you need to practice the basics, you are also welcome in this course!

I hope I can help you with this course just like I've already helped more than 5800 students with my other courses! I can't wait to see you inside! Have fun and learn a lot!

Who this course is for:

Anyone who is about to take a test/exam in the topic of Limits of Sequences
Anyone who is currently learning Calculus
Anyone who is interested in the calculation of limits

Calculus - Limits of Sequences

What you'll learn

Explore related topics

Course content

Introduction1 lecture • 2min

Theoretical introduction to sequences6 lectures • 23min

Limits of fractions5 lectures • 18min

Determination of an index number for a given closeness3 lectures • 17min

Getting rid of the square roots and cube roots4 lectures • 17min

Limits based on the definition of Euler's number (e)3 lectures • 12min

Squeeze theorem4 lectures • 11min

Thank you2 lectures • 1min

Requirements

Description

Who this course is for: