Series: Meaning, Notation, and Example
A sum of the terms of a sequence.
Definition and meaning
An infinite series is defined through the limit of its finite partial sums.
The term series names a precise mathematical idea, not merely a visual pattern. Read its notation as a statement with hypotheses, quantities, and a conclusion.
Notation
Read every symbol with its domain and hypotheses; notation compresses an argument but does not remove its conditions.
Worked example
Identify the quantities in the notation, state the relevant hypothesis, and explain what conclusion the series statement permits.
Common confusion
Do not treat series as a keyword that automatically selects a formula; its hypotheses and domain still control the conclusion.