Editing Sequence (section)

==Series==
{{Main|Series (mathematics)}}
A '''series''' is, informally speaking, the sum of the terms of a sequence. That is, it is an expression of the form <math display="inline">\sum_{n = 1}^\infty a_n</math> or <math>a_1 + a_2 + \cdots</math>, where <math>(a_n)</math> is a sequence of real or complex numbers. The '''partial sums''' of a series are the expressions resulting from replacing the infinity symbol with a finite number, i.e. the ''N''th partial sum of the series <math display="inline">\sum_{n = 1}^\infty a_n</math> is the number
:<math>S_N = \sum_{n = 1}^N a_n = a_1 + a_2 + \cdots + a_N. </math>
The partial sums themselves form a sequence <math>(S_N)_{N\in\mathbb N}</math>, which is called the '''sequence of partial sums''' of the series <math display="inline">\sum_{n = 1}^\infty a_n</math>. If the sequence of partial sums converges, then we say that the series <math display="inline">\sum_{n = 1}^\infty a_n</math> is '''convergent''', and the limit <math display="inline">\lim_{N\to\infty} S_N</math> is called the '''value''' of the series. The same notation is used to denote a series and its value, i.e. we write <math display="inline">\sum_{n = 1}^\infty a_n = \lim_{N\to\infty} S_N</math>.