bookshelf/common/Common/Sequence/Geometric.tex

\documentclass{article}
\usepackage{amsfonts, amsthm}
\usepackage{hyperref}

\newtheorem{theorem}{Theorem}
\newtheorem{custominner}{Theorem}
\newenvironment{custom}[1]{%
  \renewcommand\thecustominner{#1}%
  \custominner
}{\endcustominner}

\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}