What do you call the sum of the elements of a mathematical sequence ?
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The sum of the terms of a sequence is called a series . If a sequence is arithmetic or geometric there are formulas to find the sum of the first n terms, denoted Sn , without actually adding all of the terms.
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▶️In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
▶️Like a set, it contains members (also called elements, or terms).
▶️The number of elements (possibly infinite) is called the length of the sequence.
▶️Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter.
▶️Formally, a sequence can be defined as a function whose domain is either the set of the natural numbers (for infinite sequences), or the set of the first n natural numbers (for a sequence of finite length n).
▶️For example, (M, A, R, Y) is a sequence of letters with the letter 'M' first and 'Y' last.
▶️This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence.
▶️Sequences can be finite, as in these examples, or infinite, such as the sequence of all even positive integers (2, 4, 6, ...).
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