Convergent series

Mathematical series with a finite sum

In mathematics, a series is the sum of the terms of an infinite sequence of numbers. More precisely, an infinite sequence ( a 1 , a 2 , a 3 , …) {\displaystyle (a_{1},a_{2},a_{3},\ldots)} defines a series S that is denoted S = a 1 + a 2 + a 3 + ⋯ = ∑ k = 1 ∞ a k . {\displaystyle S=a_{1}+a_{2}+a_{3}+\cdots =\sum _{k=1}^{\infty }a_{k}.} The nth partial sum Sn is the sum of the first n terms of the sequence; that is, S n = a 1 + a 2 + ⋯ + a n = ∑ k = 1 n a k .

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