bookshelf/Bookshelf/Real/Sequence/Geometric.tex

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\documentclass{article}
2023-05-07 21:57:40 +00:00
\input{../../../preamble}
\newcommand{\link}[1]{\lean{../../..}
{Bookshelf/Real/Sequence/Geometric}
{Real.Geometric.#1}
{Real.Geometric.#1}
}
\begin{document}
\section*{Sum of Geometric Series}%
\label{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}
\link{sum\_recursive\_closed}
\end{proof}
\end{document}