# Endliche geometrische Reihe/Reell/Aufgabe/en

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Let ${\displaystyle {}x}$ be a real number, ${\displaystyle {}x\neq 1}$. Prove that for ${\displaystyle {}n\in \mathbb {N} }$ the relation

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