Sequences and series

Sequences are ordered lists of numbers following a specific rule, like the natural numbers (1, 2, 3, ...). A series is the sum of the terms in a sequence, essentially adding together elements of a sequence one by one. For example, the sequence 1, 2, 3, 4, ... has a series when we add these terms: 1 + 2 + 3 + 4 + .... Sequences help identify patterns, while series help analyze accumulations — such as totals over time or quantities. Both are foundational concepts in mathematics used to understand growth, patterns, and convergence.