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Definition: Absolutely Convergent Series

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A real series \(\sum_{k=0}^\infty x_k\) is absolutely convergent, if the series of absolute values of the summands \[\sum_{k=0}^\infty |x_k|\] is convergent.

References

[581] Forster Otto: “Analysis 1, Differential- und Integralrechnung einer Veränderlichen”, Vieweg Studium, 1983


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Learn more about the axiomatic method.

Subordinated Structure:

Propositions (4)

Cauchy Product of Absolute Convergent Serieseditcontribute as guest     
Convergence Behaviour of Absolutely Convergent Serieseditcontribute as guest     
Direct Comparison Test For Absolutely Convergent Series (Majorant Criterion)editcontribute as guest     
Ratio Test For Absolutely Convergent Serieseditcontribute as guest     

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