V2EX infinite series

Infinite Series

定义 Definition

infinite series(无穷级数):指数学中把无限多个项按顺序相加所形成的表达式,例如 \(a_1 + a_2 + a_3 + \cdots\)。无穷级数可能收敛(和趋近于某个有限值)或发散(和不趋于有限值)。

发音 Pronunciation (IPA)

/nfnt sriz/

例句 Examples

An infinite series can converge to a finite number.
无穷级数可以收敛到一个有限的数。

To compute the value of π, mathematicians often use infinite series that converge very slowly or very quickly.
为了计算圆周率 π,数学家常用收敛速度很慢或很快的无穷级数。

词源 Etymology

infinite 来自拉丁语 infinitus(“无穷的、没有界限的”),由 *in-*(否定)+ finis(界限、终点)构成;series 来自拉丁语 series(“排列、连续的序列”)。合在一起,infinite series 字面意思就是“没有终点的序列式相加”。

相关词 Related Words

文学与名著用例 Literary Works

  • G. H. Hardy Divergent Series(专门讨论发散级数与相关方法)
  • T. M. Apostol Calculus, Volume 1(微积分教材中系统讲解无穷级数)
  • Rudin Principles of Mathematical Analysis(分析学经典教材中涉及级数收敛理论)
  • Courant & John Introduction to Calculus and Analysis(以分析视角讲解级数与函数展开)
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