Infinite sequence

Definition

An infinite sequence is a list of numbers in a specific order that continues indefinitely. Each number in the list is called a term.

5 Must Know Facts For Your Next Test

1. Infinite sequences can be defined explicitly by a formula for the nth term or recursively.
2. The limit of an infinite sequence as n approaches infinity determines its convergence or divergence.
3. A sequence is said to converge if its terms approach a specific value, otherwise it diverges.
4. Common tests for convergence include the Squeeze Theorem and various comparison tests.
5. The behavior of an infinite sequence can often be visualized using graphs or tables.

Review Questions

• What does it mean for an infinite sequence to converge?
• How can you determine the limit of an infinite sequence?
• What are some common methods used to test the convergence of sequences?

Related terms

Series:

The sum of the terms of a sequence, which can be finite or infinite.

$n$th Term: A specific element in a sequence, typically denoted as $a_n$.

$\lim_{n \to \infty}$: $\text{The notation used to describe the limit of a sequence as } n \text{ approaches infinity.}$