\documentclass{article}

\input{../../../preamble}

\newcommand{\lean}[1]{\leanref
  {./Geometric.html\#Real.Geometric.#1}
  {Real.Geometric.#1}}

\begin{document}

\section{\unverified{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}

  \lean{sum\_recursive\_closed}

\end{proof}

\end{document}