Series (mathematics)
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In mathematics, a series is, informally speaking, the sum of the terms of an infinite sequence.
The sum of a finite sequence has defined first and last terms, whereas a series continues indefinitely.
Description
Given an infinite sequence (a1, a2, a3, ...), a series is informally the result of adding all those terms together: a1 + a2 + a3 + ···. These can be written more compactly using the summation symbol ∑.
A value may not always be given to such an infinite sum, and, in this case, the series is said to be divergent.
On the other hand, if the partial sum of the first terms tends to a limit when the number of terms increases indefinitely, then the series is said to be convergent, and the limit is called the sum of the series.
See also
- Continued fraction
- Convergence tests
- Convergent series
- Divergent series
- Infinite compositions of analytic functions
- Infinite expression
- Infinite product
- Iterated binary operation
- List of mathematical series
- Prefix sum
- Sequence transformation
- Series expansion
External links
- Series (mathematics @ Wikipedia
