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Example: Divergent Alternating Sequence
(related to Definition: Divergent Sequences)
The real sequence \((1)^n_{n\in\mathbb N}\): \((1,1,1,1,1,1,\ldots)\) is divergent, since it does not converge either to the number \(1\), nor to the number \(1\). It is also alternating, since the sign of its sequence members changes.
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References
Bibliography
 Forster Otto: "Analysis 1, Differential und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983