Kommutativer Ring/Endliche geometrische Reihe/Aufgabe

Es sei ${}R$ ein kommutativer Ring, ${}x\in R$ und ${}n\in \mathbb {N} _{+}$ . Zeige die Gleichheit

{}x^{n}-1=(x-1){\left(x^{n-1}+x^{n-2}+x^{n-3}+\cdots +x^{2}+x+1\right)}\,.

This article is issued from Wikiversity. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.