Proposition: Geometric Sum
For all elements $a,b\in R$ of a unit ring $R$ and all natural numbers $n$, the following sum formula (called geomertic sum) holds:
$$(a-b)\sum_{k=0}^n a^k\cdot b^{n-k}=a^{n+1}-b^{n+1}.$$
Table of Contents
Proofs: 1
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References
Bibliography
- Modler, F.; Kreh, M.: "Tutorium Analysis 1 und Lineare Algebra 1", Springer Spektrum, 2018, 4th Edition
