partial sum: meaning, definition, pronunciation and examples
C2Technical/Formal
Quick answer
What does “partial sum” mean?
The sum of the first n terms of a sequence or series.
Audio
Pronunciation
Definition
Meaning and Definition
The sum of the first n terms of a sequence or series.
In mathematics, an interim total calculated by adding a specified number of terms from a sequence; often used to approximate or analyze the convergence of an infinite series.
Dialectal Variation
British vs American Usage
Differences
No significant lexical differences. British English may favour 'series' where American might use 'sequence' in surrounding context, but 'partial sum' itself is identical.
Connotations
Identically technical in both dialects.
Frequency
Equally low-frequency and confined to technical mathematics in both regions.
Grammar
How to Use “partial sum” in a Sentence
the partial sum of [series/sequence]the [nth/first] partial sumpartial sums converge to [limit]Vocabulary
Collocations
Examples
Examples of “partial sum” in a Sentence
verb
British English
- The students were asked to partial-sum the first five terms.
American English
- The software can partial-sum the series up to any term you specify.
adjective
British English
- The partial-sum sequence is monotonic.
- She presented a partial-sum analysis.
American English
- The partial-sum sequence is monotonic.
- He used a partial-sum approach.
Usage
Meaning in Context
Business
Not used.
Academic
Primary context. Used in mathematics textbooks, papers, and lectures concerning sequences and series.
Everyday
Not used.
Technical
Core context in mathematics, engineering, physics, and computer science (especially numerical analysis).
Vocabulary
Synonyms of “partial sum”
Strong
Neutral
Weak
Vocabulary
Antonyms of “partial sum”
Watch out
Common Mistakes When Using “partial sum”
- Using 'partial sum' to mean 'part of a sum of money'.
- Misspelling as 'partial some'.
- Incorrect plural: 'partials sum' instead of 'partial sums'.
FAQ
Frequently Asked Questions
No, it is a strictly mathematical term. In finance, 'partial payment' would be used instead.
A 'sum' is a complete total. A 'partial sum' is explicitly incomplete, summing only a finite part of a potentially infinite list of terms.
For an arithmetic series, the nth partial sum is Sn = n/2 * (first term + last term), or Sn = n/2 * [2a + (n-1)d], where 'a' is the first term and 'd' is the common difference.
Yes, if the series has alternating signs, some partial sums can overshoot the final limit before converging.
The sum of the first n terms of a sequence or series.
Partial sum is usually technical/formal in register.
Partial sum: in British English it is pronounced /ˈpɑːʃəl sʌm/, and in American English it is pronounced /ˈpɑːrʃəl sʌm/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “None”
Learning
Memory Aids
Mnemonic
Think of watching a film in parts: the 'partial sum' is like the total runtime you've seen so far, not the full film.
Conceptual Metaphor
A JOURNEY TOWARDS A DESTINATION (the partial sum is the distance travelled so far; the limit of the series is the final destination).
Practice
Quiz
What does a 'partial sum' specifically refer to?