Series theory is a branch of analysis; Together with another branch of calculus, it appears in other branches as basic knowledge and tools. Both of them take limit as the basic tool, and study the object of analysis from discrete and continuous aspects, that is, the dependence between variables-function.
Chinese name
series
Foreign name
series
full name
Polynomial series
field
mathematics
meaning
It is an important tool to study functions.
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Positive series staggered series power series Cauchy criterion series convergence absolute convergence
brief introduction
A sequence is a sequence of numbers.
Project of
,
,…,
Functions connected in turn by plus signs are abbreviations of a series of items. For example:
, abbreviated as
,
A general term is called series, remember?
It is called the partial sum of series. If at any time
, the sequence Sn has a limit, and the limit is s, then the sequence converges, and
For its sum, it is recorded as
; Otherwise, it is said that the series diverges.
Series is an important tool to study functions and plays an important role in theory and practical application. This is because: on the one hand, many commonly used non-elementary functions can be expressed by series, and the solutions of differential equations are often expressed by series; On the other hand, functions can be expressed as series, so that functions can be studied by series methods, for example, non-elementary functions can be studied by power series, and approximate calculations can be made.