- Finite series
- define series
- alternating series
- Summation notation
- sigma notation
- evaluate a summation
- expand a summation
- Arithmetic series
- Geometric series
- Infinite geometric series
- partial sums
- Summary of sequence and series formulas
11.4 Essential Ideas
If the terms of sequence are added, the expression is called a series.
The indicated sum of the terms of a finite sequence s1, s2, s3, …, sn is called a finite series and is denoted by Sn = s1+ s2+s3+ … +sn.
An arithmetic series is the sum of the terms of an arithmetic sequence.
A geometric series is the sum of the terms of a geometric sequence.
If g1, g2, g3, …, g n, … is an infinite geometric sequence with a common ratio r such that |r| < 1, then the sum is denoted by G and is found by G = g1/(1 – r). If |r| is greater than or equal to 1, then the infinite geometric series has no sum.