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- In mathematics, a series is the operation of adding infinitely many numbers or quantities to a given starting number or amount12345. A sequence is an ordered list of numbers, and the numbers in this ordered list are called the elements or the terms of the sequence. A series is what you get when you add up all the terms of a sequence, and the addition, and also the resulting value, are called the sum or the summation25.Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.In mathematics, we can describe a series as adding infinitely many numbers or quantities to a given starting number or amount. We use series in many areas of mathematics, even for studying finite structures, for example, combinatorics for forming functions.byjus.com/maths/series/A "sequence" (called a "progression" in British English) is an ordered list of numbers; the numbers in this ordered list are called the "elements" or the "terms" of the sequence. A "series" is what you get when you add up all the terms of a sequence; the addition, and also the resulting value, are called the "sum" or the "summation".www.purplemath.com/modules/series.htmIn modern terminology, any (ordered) infinite sequence of terms (that is, numbers, functions, or anything that can be added) defines a series, which is the operation of adding the ai one after the other. To emphasize that there are an infinite number of terms, a series may be called an infinite series.en.wikipedia.org/wiki/Series_(mathematics)A series is a sequence of numbers where you exchange the comma with a plus or a minus. Series generally look like this: a 1 + a 2 + a 3 + … + a n + … Here, n is the number of the term and a n is the actual number in that term.www.houseofmath.com/encyclopedia/numbers-an…A series is just the sum of some set of terms of a sequence. For example, the sequence 2, 4, 6, 8,... has partial sums of 2, 6, 12, 20,... These partial sums are each a finite series. The n th partial sum of a sequence is usually called Sn.www.mathopenref.com/calcseries.html
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Sequences and Series: Terminology and Notation | Purplemath
WEBA "series" is what you get when you add up all the terms of a sequence; the addition, and also the resulting value, are called the "sum" or the "summation". For instance, "1, 2, 3, 4" is a sequence, with terms "1", "2", "3", and "4"; the corresponding series is the sum "1 …
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Sequences and Series: Basic Examples | Purplemath
WEBProvides worked examples of typical introductory exercises involving sequences and series. Demonstrates how to find the value of a term from a rule, how to expand a …
Arithmetic Series | Purplemath
WEBAn arithmetic series is the sum of the terms of an arithmetic sequence. A geometric series is the sum of the terms of a geometric sequence. There are other types of series, …
Arithmetic & Geometric Sequences | Purplemath
WEBThe two simplest sequences to work with are arithmetic and geometric sequences. An arithmetic sequence goes from one term to the next by always adding (or subtracting) …
Geometric Series | Purplemath
- Evaluate the following: ∑i=120 3(−2)i\mathbf{\color{green}{\displaystyle{ …
- Evaluate S10 for 250, 100, 40, 16,.... The notation "S10" means that I need to find the sum …
- Find a if S4=2627\color{green}{ \textbf{S}_{\mathbf{4}} = \mathbf{\frac{26}{27}} }S4=2726 …
- Show, by use of a geometric series, that 0.3333... is equal to …
- By use of a geometric series, convert 1.363636... to fractional form. First I'll break this into …
Finding sequence patterns with common differences | Purplemath
WEBA sequence is a comma-separated list; in mathematics, a sequence is a listing of numerical values. The sequence may have a rule for its comma-separated terms, or its …
Mean, median, and mode: they're ALL averages...? | Purplemath
WEBThe "mean" is the "average" you're used to, where you add up all the numbers and then divide by the number of numbers. The "median" is the "middle" value in the list of …
Digits, Numerals, Whole Numbers, and Place Value | Purplemath
WEBWe use these ten digits, along with the concept of place value, in exactly the same sense that we were using our fingers and our piles of marbles on the previous page: a certain …
What are recursive sequences? How do they work? | Purplemath
WEBA recursion is a list of values in which the later values are built from the earlier values. A recursive sequence will have one or more "seed" values, because you have to …
Conventions: What do these terms and things mean? | Purplemath
WEBFor trigonometric functions, powers are indicated directly on the function names. For instance, "the square of the sine of beta" is written as sin2(β), and this notation means …
What is the five-number summary? Learn here! | Purplemath
WEBThe five-number summary of a data set (that is, of a set of values) is the minimum value, the maximum value, and, between these two extremes, the quartile values Q1, Q2, and Q3.
Scatterplots: Correlation, Outliers, and Model Types | Purplemath
WEBPurplemath. You may be asked about the "correlation", if any, displayed within a particular scatterplot. The word orrelation can be used in at least two different ways: to refer to …
Squeezing, stretching, and squishing functions | Purplemath
WEBYou can transform function by multiplication: for a function f (x), the graphs of a×f (x) and f (a×x) will be squeezed or stretched upward or sideways.
What is function notation, and why should I care? | Purplemath
WEBFunction notation is written as follows: [function name] ( [input variable]) = [formula] For instance, the formula for the circumference C of a circle, in terms of the value of the …
What is the order of operations? Why do we need it? | Purplemath
WEBThe order of operations is parentheses (simplify inside 'em), exponents (apply 'em), multiply/divide (left to right), & add/subtract (left to right).
What are factorials, and how do they work? | Purplemath
WEBFactorials are very simple things; they're just products, and are indicated by an exclamation mark. For instance, "four factorial" is written as 4! and means the product of the whole …
What is the "natural" log, and why do we need it? | Purplemath
WEBPurplemath. A logarithm can have any positive value (other than 1) as its base, but logs with two particular bases are generally regarded as being more useful than the others: …
What are parabolas, their equations, their rules? | Purplemath
WEBA parabola is a particular type of geometrical curve which, algebraically, corresponds to a quadratic equation. In geometrical terms, the parabola corresponds to the edge of …
Matrix basics: what they are and what's their lingo | Purplemath
WEBA matrix is a square or rectangular grid of values, surrounded by square brackets. The lines of numbers going from left to right are the matrix's rows; the lines of numbers …
How are you supposed to tell even and odd functions apart?
WEBWhat are even and odd functions (in math)? An even function is one whose graph exhibits symmetry about the y -axis; an odd function is one whose graph exhibits symmetry …
What is an identity, and how do I prove it? | Purplemath
WEBTo prove an identity, you have to use logical steps to show that one side of the equation can be transformed into the other side of the equation. You do not plug values into the …
Ratios: What are They? How do They Work? | Purplemath
WEBRatios are used to create proportions by setting two ratios equal to each other and solving for some unknown, and ratios can also be used to find per-unit rates such as …
What are the 24 letters in the Greek alphabet? | Purplemath
WEBMake sure you know how to spell and pronounce at least these six Greek characters. Math uses Greek letters, such as π. You should expect to need to know at least six of the 24 …
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