infinite series
C1/C2Highly formal, technical (mathematics); occasionally metaphorical in literary/academic contexts.
Definition
Meaning
In mathematics, a sum of an infinite number of terms.
A concept in mathematics representing an unending sum of terms in a sequence; also used metaphorically to describe a process or phenomenon that seems endless or self-replicating.
Linguistics
Semantic Notes
A formal mathematical object studied in calculus and analysis. A convergent infinite series approaches a finite limit, while a divergent one does not. Metaphorical use emphasises endlessness, progression, or repetition.
Dialectal Variation
British vs American Usage
Differences
No significant lexical or grammatical differences. Pronunciation may differ slightly due to regional accent.
Connotations
Identical technical meaning. Metaphorical usage is equally rare and formal in both varieties.
Frequency
Exclusively high-frequency in advanced mathematics contexts; extremely low-frequency in general English.
Vocabulary
Collocations
Grammar
Valency Patterns
[verb] + an infinite series + [of + noun]The infinite series + [verb][adjective] + infinite seriesVocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Phrases
Idioms & Phrases
- “Not applicable; a technical term.”
Usage
Context Usage
Business
Virtually never used. Potential metaphorical use: 'The project felt like an infinite series of meetings.'
Academic
Primary context. Core concept in mathematics, physics, and engineering. E.g., 'The solution is expressed as an infinite series.'
Everyday
Extremely rare. If used, it's metaphorical: 'Parenthood is an infinite series of worries.'
Technical
Defining context. Used with precision in mathematics, computer science (e.g., power series, Fourier series).
Examples
By Part of Speech
verb
British English
- To solve the problem, we must sum the infinite series.
- One can represent the function as an infinite series.
American English
- To solve the problem, we need to sum the infinite series.
- You can represent the function as an infinite series.
adverb
British English
- The terms decrease infinitely rapidly in that series.
- The sum was calculated, in essence, series-wise to infinity.
American English
- The terms decrease infinitely quickly in that series.
- The sum was calculated, essentially, series-wise to infinity.
adjective
British English
- The infinite-series representation proved most useful.
- We studied infinite-series convergence.
American English
- The infinite-series representation was most useful.
- We studied infinite-series convergence.
Examples
By CEFR Level
- This list is very long, but an infinite series is even longer—it never ends.
- In maths, an infinite series adds up numbers forever.
- His stories felt like an infinite series of excuses.
Learning
Memory Aids
Mnemonic
Imagine a line of numbers stretching to the horizon, each waiting to be added. 'Infinite' means never-ending, 'series' means a line-up – a never-ending line-up of numbers to sum.
Conceptual Metaphor
ENDLESSNESS IS AN INFINITE SERIES (e.g., 'an infinite series of disappointments'). PROGRESS IS SUMMING A SERIES (gradual accumulation towards a goal).
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- May confuse with 'sequence' (последовательность). 'Series' here implies summation (ряд).
- The adjective 'infinite' precedes 'series' (бесконечный ряд), not the other way around.
- Avoid translating as 'endless series' in technical contexts; 'infinite' is the precise term.
Common Mistakes
- Using plural verb with 'series' (correct: 'The infinite series converges/is...'). 'Series' is singular here.
- Confusing 'infinite series' with 'infinite sequence'. A series is a sum of sequence terms.
- Omitting 'infinite' when the technical meaning is intended, leading to ambiguity.
Practice
Quiz
In which field is the term 'infinite series' primarily used?
FAQ
Frequently Asked Questions
No. Only divergent infinite series grow without bound. Convergent infinite series sum to a finite number (e.g., 1/2 + 1/4 + 1/8 + ... = 1).
It is extremely rare and would be a deliberate, metaphorical use to emphasise endless repetition, e.g., 'an infinite series of bureaucratic hurdles.'
A sequence is an ordered list of numbers. A series is the sum of the terms of a sequence. An infinite series sums infinitely many terms.
In British English: /ˌɪnfɪnət ˈsɪəriːz/. In American English: /ˌɪnfɪnət ˈsɪriz/. The stress is on the first syllable of 'infinite' and the first syllable of 'series'.