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:

$$(a-b)\sum_{k=0}^n a^k\cdot b^{n-k}=a^{n+1}-b^{n+1}.$$

| | | | | created: 2020-06-25 10:00:31 | modified: 2020-06-25 10:00:57 | by: *bookofproofs* | references: [8311]

[8311] **Modler, F.; Kreh, M.**: “Tutorium Analysis 1 und Lineare Algebra 1”, Springer Spektrum, 2018, 4. Auflage