sum of series
If a series of real or complexnumbers is convergent and the limit of its partial sums is ,then is said to be the sum of the series. Thiscircumstance may be denoted by
or equivalently
The sum of series has the distributive property
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
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.
Title | sum of series |
Canonical name | SumOfSeries |
Date of creation | 2014-02-15 19:17:15 |
Last modified on | 2014-02-15 19:17:15 |
Owner | pahio (2872) |
Last modified by | pahio (2872) |
Numerical id | 14 |
Author | pahio (2872) |
Entry type | Definition |
Classification | msc 40-00 |
Related topic | SumFunctionOfSeries |
Related topic | ManipulatingConvergentSeries |
Related topic | RemainderTerm |
Related topic | RealPartSeriesAndImaginaryPartSeries |
Related topic | LimitOfSequenceAsSumOfSeries |
Related topic | PlusSign |
Defines | partial sum |