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In mathematics, a series is, roughly speaking, an addition of infinitely many terms, one after the other. [1] The study of series is a major part of calculus and its generalization, mathematical analysis.
The nth element of an arithmetico-geometric sequence is the product of the nth element of an arithmetic sequence and the nth element of a geometric sequence. [1] An arithmetico-geometric series is a sum of terms that are the elements of an arithmetico-geometric sequence. Arithmetico-geometric sequences and series arise in various applications ...
A series is convergent if the sequence of its partial sums {, , , …} tends to a limit; that means that the partial sums become closer and closer to a given number when the number of their terms increases. More precisely, a series converges, if there exists a number such that for any arbitrarily small positive number , there is a (sufficiently ...
Arithmetic geometry can be more generally defined as the study of schemes of finite type over the spectrum of the ring of integers. [1] Arithmetic geometry has also been defined as the application of the techniques of algebraic geometry to problems in number theory. [2] See also the glossary of number theory terms at Glossary of number theory
Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic varieties. [2] [3] In more abstract terms, arithmetic geometry can be defined as the study of schemes of finite type over the spectrum of the ring of integers. [4]
The geometric series is an infinite series derived from a special type of sequence called a geometric progression.This means that it is the sum of infinitely many terms of geometric progression: starting from the initial term , and the next one being the initial term multiplied by a constant number known as the common ratio .
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