Key Concepts & Glossary
Key Equations
sum of the first [latex]n[/latex] terms of an arithmetic series | [latex]{S}_{n}=\frac{n\left({a}_{1}+{a}_{n}\right)}{2}[/latex] |
sum of the first [latex]n[/latex] terms of a geometric series | [latex]{S}_{n}=\frac{{a}_{1}\left(1-{r}^{n}\right)}{1-r}\cdot r\ne 1[/latex] |
sum of an infinite geometric series with [latex]-1<r<\text{ }1[/latex] | [latex]{S}_{n}=\frac{{a}_{1}}{1-r}\cdot r\ne 1[/latex] |
Key Concepts
- The sum of the terms in a sequence is called a series.
- A common notation for series is called summation notation, which uses the Greek letter sigma to represent the sum.
- The sum of the terms in an arithmetic sequence is called an arithmetic series.
- The sum of the first [latex]n[/latex] terms of an arithmetic series can be found using a formula.
- The sum of the terms in a geometric sequence is called a geometric series.
- The sum of the first [latex]n[/latex] terms of a geometric series can be found using a formula.
- The sum of an infinite series exists if the series is geometric with [latex]-1<r<1[/latex].
- If the sum of an infinite series exists, it can be found using a formula.
- An annuity is an account into which the investor makes a series of regularly scheduled payments. The value of an annuity can be found using geometric series.
Glossary
- annuity
- an investment in which the purchaser makes a sequence of periodic, equal payments
- arithmetic series
- the sum of the terms in an arithmetic sequence
- diverge
- a series is said to diverge if the sum is not a real number
- geometric series
- the sum of the terms in a geometric sequence
- index of summation
- in summation notation, the variable used in the explicit formula for the terms of a series and written below the sigma with the lower limit of summation
- infinite series
- the sum of the terms in an infinite sequence
- lower limit of summation
- the number used in the explicit formula to find the first term in a series
- nth partial sum
- the sum of the first [latex]n[/latex] terms of a sequence
- series
- the sum of the terms in a sequence
- summation notation
- a notation for series using the Greek letter sigma; it includes an explicit formula and specifies the first and last terms in the series
- upper limit of summation
- the number used in the explicit formula to find the last term in a series
Licenses & Attributions
CC licensed content, Specific attribution
- Precalculus. Provided by: OpenStax Authored by: OpenStax College. Located at: https://cnx.org/contents/[email protected]:1/Preface. License: CC BY: Attribution.