Endliche geometrische Reihe/Aufgabe

Sei ${}x$ eine reelle Zahl, ${}x\neq 1$ . Beweise für ${}n\in \mathbb {N}$ durch Induktion die Beziehung

{}\sum _{k=0}^{n}x^{k}={\frac {x^{n+1}-1}{x-1}}\,.

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