Sequences Definition - A function whose domain is the set of all positive integers. Finite Sequence - finite number of values or elements Infinite Sequence.

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Presentation transcript:

Sequences Definition - A function whose domain is the set of all positive integers. Finite Sequence - finite number of values or elements Infinite Sequence - infinite number of values or elements Notation - Section Sequences

Definition - A function whose domain is the set of all positive integers. Section Sequences

Three Types of Sequences Specified – enough information is given to find a pattern Explicit Formula Recursion Formula.

Section Sequences Definitions If a sequence has a limit that exists, then it is convergent and it converges to the limit value. If a sequence has a limit that does not exist, then it is divergent. Theorems.

Section Sequences

Section 10.2 – Infinite Series

Geometric Series

Section 10.2 – Infinite Series The limit does not exist, therefore it diverges. The limit does not equal 0, therefore it diverges. The limit equals 0, therefore the n th – Term Test for Divergence cannot be used.

Section 10.2 – Infinite Series

Telescoping Series (collapsing series)