Arithmetic series

Contents
1 Definition
2 Formulas
3 See also
4 Links

Definition

In mathematics, an arithmetic series is the sum of the components of an arithmetic progression.

Formulas

Formulas for arithmetic series usually use Sn to represent the sum of the first nth terms of an arithmetic progression, an for the nth term of the arithmetic progression, and d for the common difference between the terms of the arithmetic progression. The formula to determine the sum of the first nth terms of an arithmetic progression is:

S_n = \frac{n}{2} [ 2a_1 + (n-1)d ]

An often-told story is that Gauss discovered this formula when his third grade teacher asked the class to find the sum of the first 100 numbers, and he instantly computed the answer (5050).

See also

- Arithmetic progression

Links

- Arithmetic Series (from Wolfram MathWorld)

See also: Arithmetic series, Arithmetic progression, Carl Friedrich Gauss, Mathematics