bookshelf/Common/Real/Sequence/Geometric.tex

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\documentclass{article}
2023-05-07 21:57:40 +00:00
\input{../../../preamble}
\newcommand{\lean}[1]{\href
{./Geometric.html\#Real.Geometric.#1}
{Real.Geometric.#1}}
\begin{document}
\section{\proceeding{Sum of Geometric Series}}%
\hyperlabel{sec:sum-geometric-series}%
Let $(a_i)_{i \geq 0}$ be a geometric sequence with common ratio $r \neq 1$.
Then for some $n \in \mathbb{N}$,
$$\sum_{i=0}^n a_i = \frac{a_0(1 - r^{n+1})}{1 - r}.$$
\begin{proof}
\lean{sum\_recursive\_closed}
\end{proof}
\end{document}