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单词 SumOfSeries
释义

sum of series


If a series n=1an of real or complexnumbers is convergentMathworldPlanetmathPlanetmath and the limit of its partial sums is S,then S is said to be the sum of the series.  Thiscircumstance may be denoted by

n=1an=S

or equivalently

a1+a2+a3+=S.

The sum of series has the distributive property

c(a1+a2+a3+)=ca1+ca2+ca3+

with respect to multiplication.  Nevertheless, one must notthink that the sum series means an addition of infinitely manynumbers — it’s only a question of the limit

limn(a1+a2++an)partial sum.

See also the entry “manipulating convergent series”!

The sum of the series is equal to the sum of a partial sum andthe corresponding remainder term.

Titlesum of series
Canonical nameSumOfSeries
Date of creation2014-02-15 19:17:15
Last modified on2014-02-15 19:17:15
Ownerpahio (2872)
Last modified bypahio (2872)
Numerical id14
Authorpahio (2872)
Entry typeDefinition
Classificationmsc 40-00
Related topicSumFunctionOfSeries
Related topicManipulatingConvergentSeries
Related topicRemainderTerm
Related topicRealPartSeriesAndImaginaryPartSeries
Related topicLimitOfSequenceAsSumOfSeries
Related topicPlusSign
Definespartial sum
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更新时间:2025/5/4 21:55:35