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Proof

(related to Proposition: Convergent Complex Sequences Are Cauchy Sequences)

• This is a special case of an even more general result bout metric spaces that all convergent sequences are also Cauchy sequences.
• Now, it follows immediately from the distance of complex numbers makes them a metric space.
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References

Bibliography

1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983