ProofWiki:Sandbox

Theorem
Let $x$ be an element of one of the standard number fields: $\Q, \R, \C$ such that $x \ne 1$.

Let $n \in \N_{>0}$.

Then:
 * $\displaystyle \sum_{j \mathop = 0}^{n - 1} jx^{j} = \frac{ \left({ n - 1 }\right)x^{n + 1} - nx^{n} + x }{ \left({ x - 1 }\right)^{2} }$