Math 1522 - Sequences

Flashcards covering key vocabulary and concepts related to sequences in mathematics.

Sequence

An ordered set of numbers of the form {a₁, a₂, a₃, …} where anv are the terms of the sequence.

Recurrence relation

A relation that defines each term in the sequence in terms of the preceding terms.

Explicit formula

A formula that defines the nth term of the sequence directly.

Convergence

A condition in which the terms of a sequence approach a specific limit L as n approaches infinity.

Divergence

A condition in which the terms of a sequence do not approach any limit as n approaches infinity.

Limit L

The value that the terms of a sequence can get arbitrarily close to as n becomes sufficiently large.

Monotonic sequence

A sequence that is either entirely non-increasing or non-decreasing.

Bounded sequence

A sequence where all terms are confined within a fixed upper and lower limit.

Squeeze Theorem

A principle that allows you to find the limit of a sequence by 'squeezing' it between two other sequences that converge to the same limit.

Increasing sequence

A sequence where each term is less than the next term, i.e., an < an+1 for all n.

Decreasing sequence

A sequence where each term is greater than the next term, i.e., an > an+1 for all n.

Limit laws for sequences

Rules that describe how limits behave under various operations such as addition, multiplication, and division.

DNE (Does Not Exist)

A term used to indicate that a limit or value is not defined.