几何级数英文解释翻译、几何级数的近义词、反义词、例句

关键字：

英语翻译：

【计】 geometric progression
【经】 geometric progression

分词翻译：

几何的英语翻译：

geometry; how many; how much

级数的英语翻译：

progression; series
【经】 progression

网络扩展解释

几何级数

几何级数（jǐ hé jí shù）又称等比数列求和，是数学中重要的级数之一。几何级数由公比连乘而成，它的通项公式可表示为a_n = a₁ * r^n-1，其中a₁为初始项，r为公比，n为项数。几何级数收敛的条件是公比r小于1，而发散的条件是r大于或等于1。

英文解释翻译

Geometric series

英文读音

[ˌdʒiːəʊˈmetrɪk ˈsɪəriːz]

英文用法

The sum of a geometric series is given by the formula S_n = a₁ * (1 - rⁿ) / (1 - r), where S_n is the sum of the first n terms of the series, a₁ is the initial term, and r is the common ratio. The formula is valid only for r not equal to 1.

英文例句

• The sum of the geometric series 1, 2, 4, 8, 16, ... is 31.
• The geometric series 3, 6, 12, 24, ... has a common ratio of 2.
• A geometric series can be used to calculate the value of an annuity.

英文近义词

• Geometric progression: a sequence of numbers in which each term after the first is obtained by multiplying the preceding term by a fixed factor.
• Infinite geometric series: a geometric series with an infinite number of terms.

英文反义词

• Arithmetic series: a sequence of numbers in which each term is obtained by adding a fixed amount to the preceding term.

英文单词常用度

根据Google Ngram Viewer的统计， "geometric sequence"的使用频率远高于"geometric series"，但"geometric series"的使用频率也一直保持着稳定的上升趋势。

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