Arithmetic series
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Definition
In mathematics, an arithmetic series is the sum of the components of an arithmetic progression.
Formulas
Formulas for arithmetic series usually use <math>S_n<math> to represent the sum of the first nth terms of an arithmetic progression, <math>a_n<math> 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:
- <math>S_n = \frac{n}{2} [ 2a_1 + (n-1)d ]<math>
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) (http://mathworld.wolfram.com/ArithmeticSeries.html)