“series”的概念、定义、习题解题方法及翻译-数学辞典

单词

series

释义

series

A finite series of length n is written as a1+a2+…+an, where a1, a2,…, an are n numbers called the terms in the series. The sum of the series is simply the sum of the n terms.

An infinite series is written as a1+a2+a3+…, with terms a1, a2, a3,…, one corresponding to each positive integer. The nth partial sum is sn, the sum of the first n terms. If the sequence s1, s2, s3,…has a limit s, then the value s is called the sum (or sum to infinity) of the infinite series. Otherwise, the infinite series is said to diverge. For a list of important series and convergence tests, see appendix 11 and appendix 12. See also algebra of limits, arithmetic series, geometric series, partial sum, Taylor series.

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