bookshelf/common/Common/Sequence/Geometric.tex

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\documentclass{article}
\input{../../preamble}
\begin{document}
\begin{theorem}[Sum of Geometric Series]
Let $(a_i)_{i \geq 0}$ be a geometric sequence with common ratio $r \neq 1$.
Then for some $n \in \mathbb{N}$,
$$\sum_{i=0}^n a_i = \frac{a_0(1 - r^{n+1})}{1 - r}.$$
\end{theorem}
\begin{proof}
\href{Geometric.lean}{Common.Sequence.Geometric.sum_recursive_closed}
\end{proof}
\end{document}