Mathematical series | Convergence (mathematics)
In mathematics, a series is the sum of the terms of an infinite sequence of numbers. More precisely, an infinite sequence defines a series S that is denoted The nth partial sum Sn is the sum of the first n terms of the sequence; that is, A series is convergent (or converges) if the sequence of its partial sums tends to a limit; that means that, when adding one after the other in the order given by the indices, one gets partial sums that become closer and closer to a given number. More precisely, a series converges, if there exists a number such that for every arbitrarily small positive number , there is a (sufficiently large) integer such that for all , If the series is convergent, the (necessarily unique) number is called the sum of the series. The same notation is used for the series, and, if it is convergent, to its sum. This convention is similar to that which is used for addition: a + b denotes the operation of adding a and b as well as the result of this addition, which is called the sum of a and b. Any series that is not convergent is said to be divergent or to diverge. (Wikipedia).
Introduction to Infinite Series
This video introduces infinite series and the concept of a converging and diverging series. http://mathispower4u.yolasite.com/
From playlist Infinite Sequences and Series
What Does It Mean For A Series To Converge?
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys What Does It Mean For A Series To Converge? A series convergences to S if the sequence of partial sums converges to S. In this video I try to explain it and give an example. The example given is a version of Zeno's Dichotomy Paradox
From playlist Calculus 2 Exam 4 Playlist
Ex 1: Infinite Series - P Series Test (Convergent) and Find a Partial Sum
This video explains how to apply the p-series test to determine if an infinite series is convergent or divergent. Site: http://mathispower4u.com
From playlist Infinite Series
Ex 1: Telescoping Series (Convergent)
This video explains how to determine if a telescoping series converges or diverges. If it converges the sum is found. Site: http://mathispower4u.com
From playlist Infinite Series
Definition and examples of series. In this video, I define the notion of a series using partial sums, and give a couple of examples of series. I also show the fact used in many times in calculus that a series converges if and only if it is bounded, which is used many times in calculus. Enj
From playlist Series
Ex: Infinite Series - Direct Comparison Test (Convergent)
This video provides an example of how to apply the direct comparison test to determine if an infinite series is convergent, divergent, or if the test is inconclusive. Site: http://mathispower4u.com
From playlist Infinite Series
This videos shows how to determine if an infinite geometric series converges or diverges. http://mathispower4u.yolasite.com/
From playlist Infinite Sequences and Series
Convergent sequences are bounded
Convergent Sequences are Bounded In this video, I show that if a sequence is convergent, then it must be bounded, that is some part of it doesn't go to infinity. This is an important result that is used over and over again in analysis. Enjoy! Other examples of limits can be seen in the
From playlist Sequences
This video explains how to if a telescoping series converges and what it converges to. http://mathispower4u.yolasite.com/
From playlist Infinite Sequences and Series
Worldwide Calculus: Theorems on Series III: Series with Positive and Negative Terms
Lecture on 'Theorems on Series III: Series with Positive and Negative Terms' from 'Worldwide Integral Calculus' and 'Worldwide AP Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Worldwide Single-Variable Calculus for AP®
Worldwide Calculus: Theorems on Series II: Non-negative Series
Lecture on 'Theorems on Series II: Non-negative Series' from 'Worldwide Integral Calculus' and 'Worldwide AP Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Worldwide Single-Variable Calculus for AP®
Calculus 11.6 Absolute Convergence, Ratio and Root Tests
My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart
From playlist Calculus
Calculus 2, Alternating series (April 13, 2021)
This is a recording of a live class for Math 1172, Calculus 2, an undergraduate course for math majors at Fairfield University, Spring 2021. Class website: http://cstaecker.fairfield.edu/~cstaecker/courses/2021s1172/
From playlist Math 1172 (Calculus 2) Spring 2021
Calculus BC - Unit 4 Lesson 6: Absolute and Conditional Convergence
AP Calculus BC - Unit 4: Sequences and Series - Lesson 6: Absolute and Conditional Convergence
From playlist AP Calculus BC
This lecture is on Calculus II. It follows Part II of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.
From playlist Calculus II
Worldwide Calculus: Theorems on Series I: Basic Properties
Lecture on 'Theorems on Series I: Basic Properties' from 'Worldwide Integral Calculus' and 'Worldwide AP Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Worldwide Single-Variable Calculus for AP®
Power Series - Finding The Radius & Interval of Convergence - Calculus 2
This calculus video tutorial provides a basic introduction into power series. it explains how to find the radius of convergence and the interval of convergence of a power series using the ratio test. If the limit of the ratio test is zero, the power series converges for all x values. If
From playlist New Calculus Video Playlist
Lecture 10: The Completeness of the Real Numbers and Basic Properties of Infinite Series
MIT 18.100A Real Analysis, Fall 2020 Instructor: Dr. Casey Rodriguez View the complete course: http://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/ YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61O7HkcF7UImpM0cR_L2gSw We introduce Cauchy sequences and prove the
From playlist MIT 18.100A Real Analysis, Fall 2020
Math 031 032017 Introduction to Infinite Series
Introduction. Sequence of partial sums. Examples of sequences of partial sums. Definition of convergence of an infinite series. Canonical example: geometric series. Ubiquitous (but unnoticed) example: infinite decimal expansion. Series and basic arithmetic (addition and scalar multip
From playlist Course 3: Calculus II (Spring 2017)
Absolute Convergence, Conditional Convergence, and Divergence
This calculus video tutorial provides a basic introduction into absolute convergence, conditional convergence, and divergence. If the absolute value of the series convergences, then the original series will converge based on the absolute convergence test. If the absolute value of the ser
From playlist New Calculus Video Playlist