Definition: Convergent Serieseditcontribute as guest [id:175]Notation show notationA real series \(\sum_{k=0}^\infty x_k\) is called convergent, if the real sequence \((s_n)_{n\in\mathbb N}\) of partial sums \[s_n:=\sum_{k=0}^n x_k,\quad\quad n\in\mathbb N\] is convergent. For convergent real series, the notation \[\sum_{k=0}^\infty x_k\] can, depending on the context, denote two things:
References [581] Forster Otto: “Analysis 1, Differential- und Integralrechnung einer Veränderlichen”, Vieweg Studium, 1983 All logical predecessors and all successors of the current node are: Found a mistake? Fix it by editing the definition above!Learn more about the axiomatic method. Subordinated Structure: Propositions (5)
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