Alternating Sequences

Definition A sequence is said to be alternating or oscillating if it is divergent, but it neither diverges to infinity or to minus infinity. An alternating sequence can be bounded, such as, or unbounded, such as

Example (1) Alternating sequence does not mean it alternates between positive and negative terms

Example (2) Alternating sequence does not mean alternating between positive and negative terms

Example (3) =

Example (4) = is bounded, since │cos(n/2 │≤ 1

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