Samlagningarröð

Samlagningarröð, a term originating from Icelandic, directly translates to "addition series." In mathematics, it refers to a sequence of numbers where each term is obtained by adding a constant value to the previous term. This constant value is known as the common difference. For example, a sequence like 2, 4, 6, 8, 10 is a samlagningarröð with a common difference of 2.

The general form of a samlagningarröð can be represented by the formula a_n = a_1 + (n-1)d, where a_n is the n-th term, a_1 is the first term, n is the position of the term in the sequence, and d is the common difference. This formula allows for the calculation of any term in the series without having to list all the preceding terms. The sum of the first n terms of a samlagningarröð can also be calculated using specific formulas, often involving the first and last term, or the first term and the common difference. These series are fundamental in various areas of mathematics and have practical applications in fields such as finance for calculating simple interest or in physics for describing uniformly accelerated motion.

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