Infinite Sequences & Series

Infinite Sequences: Overview

Definition of Sequence: list of numbers following a definite order

denoted by either or

Fibonacci Sequence

:

,

,

for

Ie. Each term is sum of two preceding terms.

Sequence has a limit if ; ie. as , then it converges. Otherwise diverges.

Sequence is increasing if for all ; ie

If it is decreasing if for all ; ie

If neither increasing or decreasing, it is monotonic.

Bounded Sequence: if for all .

If only one side is bound, its called bounded below or above.

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