série

Série is a term used in Portuguese and several other languages to denote an ordered collection of items and, depending on the context, has distinct meanings in mathematics, statistics, broadcasting, and everyday language. In many cases it refers to a sequence or the result obtained by summing a sequence of terms.

In mathematics, a série (series) is the sum of the terms of a sequence. A sequence lists numbers a1, a2, a3, ... while the série is the accumulation a1 + a2 + a3 + ... Finite séries have a finite sum; infinite séries may converge to a finite limit under certain conditions. The notation uses the summation symbol ∑. Common examples include séries aritméticas and séries geométricas. For instance, the geometric série ∑_{k=0}^{∞} ar^k converges to a/(1−r) when |r| < 1, and the partial sums of a geometric series are S_n = a1(1−r^n)/(1−r). For séries infinitas, convergence tests such as comparison, ratio, and root tests are employed to determine whether a limit exists.

In statistics and data analysis, a time series (série temporal) is a sequence of observations collected at successive points in time, used to analyze trends, seasonality, and forecasting. In other contexts, the term Série can refer to a series of related works, such as a book series or a product line.

In popular culture, a televisão series or TV series is a set of episodes sharing a common universe or narrative, released over time and designed to be watched in sequence or as independent installments. The term may also appear in other specialized fields, always indicating a structured progression or collection of elements.