Ratios | Articles containing proofs | Geometric series
In mathematics, a geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms. For example, the series is geometric, because each successive term can be obtained by multiplying the previous term by . In general, a geometric series is written as , where is the coefficient of each term and is the common ratio between adjacent terms. The geometric series had an important role in the early development of calculus, is used throughout mathematics, and can serve as an introduction to frequently used mathematical tools such as the Taylor series, the complex Fourier series, and the matrix exponential. The name geometric series indicates each term is the geometric mean of its two neighboring terms, similar to how the name arithmetic series indicates each term is the arithmetic mean of its two neighboring terms. The sequence of geometric series terms (without any of the additions) is called a geometric sequence or "geometric progression". (Wikipedia).
This video introduces geometric series. http://mathispower4u.yolasite.com/
From playlist Series (Algebra)
Learn how to determine the sum of a geometric finite series
👉 Learn how to find the geometric sum of a series. A series is the sum of the terms of a sequence. A geometric series is the sum of the terms of a geometric sequence. The formula for the sum of n terms of a geometric sequence is given by Sn = a[(r^n - 1)/(r - 1)], where a is the first term
From playlist Series
How to determine the sum of an finite geometric series
👉 Learn how to find the geometric sum of a series. A series is the sum of the terms of a sequence. A geometric series is the sum of the terms of a geometric sequence. The formula for the sum of n terms of a geometric sequence is given by Sn = a[(r^n - 1)/(r - 1)], where a is the first term
From playlist Series
Given a geometric series, write in summation notation
👉 Learn how to write the sum from a geometric series. A series is the sum of the terms of a sequence. A geometric series is the sum of the terms of a geometric sequence. The formula for the sum of n terms of a geometric sequence is given by Sn = a[(r^n - 1)/(r - 1)], where a is the first t
From playlist Series
Using summation notation to express the sum of a geometric series
👉 Learn how to write the sum from a geometric series. A series is the sum of the terms of a sequence. A geometric series is the sum of the terms of a geometric sequence. The formula for the sum of n terms of a geometric sequence is given by Sn = a[(r^n - 1)/(r - 1)], where a is the first t
From playlist Series
Determining the sum of a geometric sum when there is no sum
👉 Learn how to find the geometric sum of a series. A series is the sum of the terms of a sequence. A geometric series is the sum of the terms of a geometric sequence. The formula for the sum of n terms of a geometric sequence is given by Sn = a[(r^n - 1)/(r - 1)], where a is the first term
From playlist Series
Evaluating the partial sum of a geometric series
👉 Learn how to find the geometric sum of a series. A series is the sum of the terms of a sequence. A geometric series is the sum of the terms of a geometric sequence. The formula for the sum of n terms of a geometric sequence is given by Sn = a[(r^n - 1)/(r - 1)], where a is the first term
From playlist Series
How to determine the sum of a infinite geometric series
👉 Learn how to find the geometric sum of a series. A series is the sum of the terms of a sequence. A geometric series is the sum of the terms of a geometric sequence. The formula for the sum of n terms of a geometric sequence is given by Sn = a[(r^n - 1)/(r - 1)], where a is the first term
From playlist Series
Expressing the sum using sum notation of a geometric series
👉 Learn how to write the sum from a geometric series. A series is the sum of the terms of a sequence. A geometric series is the sum of the terms of a geometric sequence. The formula for the sum of n terms of a geometric sequence is given by Sn = a[(r^n - 1)/(r - 1)], where a is the first t
From playlist Series
Geometric Series and Geometric Sequences - Basic Introduction
This algebra and precalculus video tutorial provides a basic introduction into geometric series and geometric sequences. It explains how to calculate the common ratio of a geometric sequence and how to determine the nth term of a geometric sequence. It explains how to write a general equ
From playlist New Calculus Video Playlist
Convergence of a geometric series (KristaKingMath)
► My Sequences & Series course: https://www.kristakingmath.com/sequences-and-series-course Learn how to determine whether a geometric series converges or diverges and if it converges, how to find its sum. ● ● ● GET EXTRA HELP ● ● ● If you could use some extra help with your math class,
From playlist Sequences & Series
From Zero to Geo Introduction (Geometric Algebra Series)
This video is the introduction to my series on geometric algebra, From Zero to Geo. In this series, we will build geometric algebra from the ground up, starting from just high school algebra. My hope is that this series can be used by motivated high schoolers (or anybody above that level
From playlist From Zero to Geo
Calculus II - 9.2.2 The Geometric Series
This is our first "special" series we will learn. Be sure to keep track of what makes a series Geometric, and the conclusion we can draw based on the value of r. Calculus I playlist corresponds to chapters 1-5 of Calculus 11e, Larson, Edwards: https://www.youtube.com/playlist?list=PLl-gb0
From playlist Calculus II (Entire Course)
Finding the limit of simple series, such as the harmonic series and geometric series
From playlist 242 spring 2012 exam 3
what is your mental model of math?
Most people rarely, if ever, think about their mental models but having a good mental model about a subject enables the development of expertise in that subject. This video proposes a mental model about an area of mathematics. The model is actionable, simple, and hierarchical. Contents: 0
From playlist Summer of Math Exposition 2 videos
Power Series Representation of Functions Calculus 2 BC
I work through four examples of finding Geometric Powers Series to represent a given function about a center c. The third and fourth examples use Operations with Power Series, Partial Fractions, and finding the integral of a series. Example 1 at 1:47 Example 2 at 6:23 Example 3 involving
From playlist Calculus 2
Converting Repeating Decimals into Fractions
In this video, I cover how to convert repeating decimals into fractions using an infinite geometric series as well as doing it in a more algebraic way. I tried to start from the basics so that anyone who didn't know the sum of an infinite geometric series would not be in pure confusion. La
From playlist Summer of Math Exposition Youtube Videos
Arithmetic Sequences and Arithmetic Series - Basic Introduction
This video provides a basic introduction into arithmetic sequences and series. It explains how to find the nth term of a sequence as well as how to find the sum of an arithmetic sequence. It also discusses how to distinguish a finite sequence from an infinite series. It also includes a
From playlist New Precalculus Video Playlist
What is the formula to find the sum of an arithmetic sequence
👉 Learn all about series. A series is the sum of the terms of a sequence. Just like in sequences, there are many types of series, among which are: arithmetic and geometric series. An arithmetic series is the sum of the terms of an arithmetic sequence. A geometric series is the sum of the t
From playlist Series
Does sum (n^5)/(4^n) converge? - Week 3 - Lecture 1 - Sequences and Series
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From playlist Ohio State: Calculus Two with Jim Fowler: Sequences and Series | CosmoLearning Mathematics