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In mathematics, a series is, roughly speaking, the operation of adding infinitely many quantities, one after the other, to a given starting quantity. [ 1] The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathematics, even for studying finite structures (such as in ...
Sequence. In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called elements, or terms ). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, the same elements can appear multiple times at different ...
List of mathematical series. This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. is a Bernoulli polynomial. is an Euler number. is the Riemann zeta function. is the gamma function. is a polygamma function. is a polylogarithm.
Arithmetic progression. An arithmetic progression or arithmetic sequence (AP) is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that arithmetic progression. For instance, the sequence 5, 7, 9, 11, 13 ...
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 n th partial sum Sn is the sum of the first n terms of the sequence; that is, A series is convergent (or converges) if and only if the sequence of its partial sums tends to a limit ...
Sequences and series. Wikimedia Commons has media related to Sequence. In mathematics, a sequence is a list of objects (or events) which have been ordered in a sequential fashion; such that each member either comes before, or after, every other member. More formally, a sequence is a function with a domain equal to the set of positive integers .
Telescoping series. In mathematics, a telescoping series is a series whose general term is of the form , i.e. the difference of two consecutive terms of a sequence . [ 1] As a consequence the partial sums only consists of two terms of after cancellation. [ 2][ 3] The cancellation technique, with part of each term cancelling with part of the ...
In mathematics, the limit of a sequence is the value that the terms of a sequence "tend to", and is often denoted using the symbol (e.g., ). [ 1] If such a limit exists, the sequence is called convergent. [ 2] A sequence that does not converge is said to be divergent. [ 3]
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