Aufgabe 10.1. Betrachten Sie die Folge \sqrt{2}, \sqrt{2+\sqrt{2}}, \sqrt{2+\sqrt{2+\sqrt{2}}}, ... Zeigen Sie, dass die Folge konvergiert, und bestimmen Sie den Grenzwert.
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The given sequence is β(2+β(2+β(2+...))). To show that the sequence converges, we need to prove that it has a limit. Let's assume that the limit of the sequence is L. Now, let's consider the expression inside the square root: 2+β(2+β(2+β(2+...))). We can see Show moreβ¦
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