geometric series

IPA/dʒˌiːəʊmˈɛtɹɪk sˈiəɹiz/
IPA/dʒˌiːoʊmˈɛtɹɪk sˈɪɹiz/

geometric series — 名詞

1. a sequence of numbers where each term after the first is the previous term multi

1.名詞B2
釋義

幾何級數

各項成等比數列的級數

a sequence of numbers where each term after the first is the previous term multiplied by a fixed number (the ratio), and the terms are written as a sum; for example, 5 + 10 + 20 + 40 is a geometric series with ratio 2, while 27 + 9 + 3 + 1 has ratio 1/3.

例句

Renata modelled a bouncing ball using a geometric series with a fixed rebound ratio.

Renata 利用固定反彈比的幾何級數來模擬一顆彈跳球的運動。

geometric series with a fixed [ratio]

Jiwoo expressed 0.8888… as the geometric series 0.8 + 0.08 + 0.008 + …, which equals 8/9.

Jiwoo 將循環小數 0.8888… 表示為幾何級數 0.8 + 0.08 + 0.008 + …，該級數等於 8/9。

repeating decimal expressed as a geometric series

反義詞
  • arithmetic series

    a sum of terms with a constant difference rather than a constant ratio

文法句型

a geometric series + of + [number]

用法筆記

Distinguish from an arithmetic series, where the difference between consecutive terms is constant (e.g., 5 + 10 + 15 + 20). In a geometric series the ratio between terms is constant — check whether you are adding a fixed number (arithmetic) or multiplying by a fixed number (geometric).

常見錯誤

❌The sequence 5, 10, 15, 20 forms a geometric series.
✅The sequence 5, 10, 15, 20 forms an arithmetic series.
💡In a geometric series each term is multiplied by a fixed ratio, but here the difference between consecutive terms is a constant 5, making it an arithmetic series.