Introduction to Sequence and Series

Vocabulary flashcards covering the definitions and notations of sequences and series based on the lecture transcript.

Sequence

An ordered list of numbers that follows a certain pattern.

Term

The name given to every number in a sequence.

Finite Sequence

A number sequence that has a first and last term, meaning it has a definite number of terms.

Infinite Sequence

A number sequence that has a first term but no last term.

Ellipsis

The symbol ($...$) commonly used in an infinite sequence to denote unknown next terms.

General Statement

An algebraic expression that is used to identify the terms of a sequence according to their order.

$$a_n$$

The symbol read as the $n\text{th}$ term, where $n$ is the order number of the term.

Series

The indicated sum of the terms in a finite sequence, denoted by $S_n$.

Summation Notation

A method of representing a series denoted by the sigma ($\sum$) symbol which means sum.

Index of Summation ($i$)

In summation notation, this variable represents the starting term.

$n$ (in Summation)

The variable in summation notation representing the last term of the series.