Series (mathematics)

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History of the theory of infinite series

Philosophy of motion Zeno's paradoxes Achilles and the tortoise Actual infinity Absurdity

71 related topics

Convergence testing

⁠ n {\displaystyle n} ⁠th-term test Telescoping sum Basel problem Direct comparison test Limit comparison test

20 related topics

Series of functions

Pointwise convergent Uniform convergence Weierstrass' M-test Abel's uniform convergence test Dini's test

44 related topics

Summations over general index sets

Index set Formal sum Counting measure Cardinality Countable

38 related topics

Topics to explore

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Overview

Mathematics
Addition
Infinity
Terms Addend
Calculus
Mathematical analysis
Combinatorics
Generating functions Generating function
Physics
Computer science
Statistics
Finance
Ancient Greeks Ancient Greece
Potentially infinite Potential infinity
Finite sums Summation
Paradoxical Paradox
Zeno's paradoxes
Archimedes
Quadrature of the parabola
Limits Limit (mathematics)
Isaac Newton
Carl Friedrich Gauss
Augustin-Louis Cauchy
Completeness of the real numbers
Absolute convergence
Conditional convergence
Infinite sequence Sequence (mathematics)
Functions Function (mathematics)
Matrices Matrix (mathematics)
Finite series

Definition

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Map overview Semantic statistics

Nodes291

Edges290

Triples12

Avg. degree1.99

Density0.006873

Components1

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Important terminology Word statistics

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Important terminology

series displaystyle sum terms sums infty finite convergence partial convergent sequence limit converges numbers textstyle infinite also cdots functions addition

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
physics	instance of	The mathematical properties of infinite series make them widely applicable in other quantitative disciplines	0.80	text
computer science	instance of	The mathematical properties of infinite series make them widely applicable in other quantitative disciplines	0.80	text
statistics	instance of	The mathematical properties of infinite series make them widely applicable in other quantitative disciplines	0.80	text
finance.Among the Ancient Greeks	instance of	The mathematical properties of infinite series make them widely applicable in other quantitative disciplines	0.80	text
the idea that a potentially infinite summation could produce a finite result was considered paradoxical	instance of	The mathematical properties of infinite series make them widely applicable in other quantitative disciplines	0.80	text
most famously in Zeno's paradoxes	instance of	The mathematical properties of infinite series make them widely applicable in other quantitative disciplines	0.80	text
Leonhard Euler operated liberally with infinite series	instance of	mathematicians	0.80	text
even if they were not convergent	instance of	mathematicians	0.80	text
addition	instance of	if the terms support appropriate structure then it is possible to define operations	0.80	text
multiplication	instance of	if the terms support appropriate structure then it is possible to define operations	0.80	text
derivative	instance of	if the terms support appropriate structure then it is possible to define operations	0.80	text
antiderivative for power series	instance of	if the terms support appropriate structure then it is possible to define operations	0.80	text

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History of the theory of infinite series

Convergence testing

Series of functions

Summations over general index sets

Key facts & relationships

Topics to explore

Overview

Definition

Grouping and rearranging terms

Operations

Examples of numerical series

Convergence testing

Sums of divergent series

Series of functions

History of the theory of infinite series

Summations over general index sets

Advanced semantic analysis

Map overview Semantic statistics