几何级数 (jǐ hé jí shù) — geometric progression; geometric series

Definition

A math term for a sequence where each term is the previous one multiplied by a fixed ratio (e.g. 2, 4, 8, 16). Contrast with 算术级数 (arithmetic progression), which adds a fixed difference instead.

noun
geometric progressiongeometric series

Examples

  • 几何级数，。
    Zhè ge jǐ hé jí shù zēng zhǎng dé hěn kuài, měi gè shù shì qián yí gè shù de liǎng bèi.
    This geometric progression grows very fast; each number is twice the previous one.
  • 几何级数nS=a(1-r^n)/(1-r)。
    Jì suàn jǐ hé jí shù qián n xiàng hé de gōng shì shì S=a (1-r^n) / (1-r).
    The formula for the sum of the first n terms of a geometric series is S=a(1-r^n)/(1-r).
  • 几何级数，。
    jǐ hé jí shù Hé suàn shù jí shù bù yí yàng, tā shì àn gù dìng bǐ lì zēng jiā de.
    Geometric progressions are different from arithmetic progressions; they increase by a fixed ratio.

Origin

Compound word
构词法gòucífǎ
偏正piānzhèngModifier + head

The first part narrows down the second: it says what kind of thing the head is.

几何geometry
几jǐhow many何héwhat
联合Side by side
级数series
级jírank数shùnumber
偏正Modifier + head

几何 (geometric) describes 级数 (series), a sequence whose terms grow by a fixed ratio.

Characters in this word

Two or more meaningful parts placed together so that their meanings combine into a new one.

This origin belongs to the traditional form 幾; 几 is its simplified writing.

  • 𢆶𢆶𢆶silk threads; little things
  • 戍戍shùto guard against

The traditional form 幾 puts 𢆶 (silk threads; little things) and 戍 (to guard against) together to show watching over the fine details; the simplified 几 is a later abbreviation.

Open 几 →

Two or more meaningful parts placed together so that their meanings combine into a new one.

The old form of 何 drew a person carrying something on their shoulder. If the carried thing was a 戈, the 人 and 戈 parts together showed that picture.

Open 何 →

Most characters — around four in five — are built this way: one part hints at the meaning, the other at the pronunciation.

This origin belongs to the traditional form 級; 级 is its simplified writing.

Meaning part形符xíngfú
糹Written in full as糸mìthread
Sound part声符shēngfú
及
及jí級jí
Same sound today

The traditional form 級 has 糹 (thread) and 及 as a sound part; its original sense was a sequence related to silk. The simplified 级 is a later shorthand.

Open 级 →

Most characters — around four in five — are built this way: one part hints at the meaning, the other at the pronunciation.

This origin belongs to the traditional form 數; 数 is its simplified writing.

Meaning part形符xíngfú
攴攴pū
Sound part声符shēngfú
婁
婁lóu數shù(r)
The sound has drifted apartThe sound part was a clue two thousand years ago — it often still helps, but not always.

The traditional form 數 pairs 攴, the meaning part, with 婁, the sound part; the simplified 数 is a shorthand.

Open 数 →

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