Rationale Folge/Künstliche Summe/Aufgabe/Lösung

Es ist

{}z_{n}={\frac {1-n^{2}}{n}}+n={\frac {1-n^{2}}{n}}+{\frac {n^{2}}{n}}={\frac {1-n^{2}+n^{2}}{n}}={\frac {1}{n}}\,,

die Folge konvergiert also gegen

{}0

.

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