24 lines
466 B
TeX
24 lines
466 B
TeX
\documentclass{article}
|
|
\usepackage{amsfonts, amsthm}
|
|
\usepackage{hyperref}
|
|
|
|
\newtheorem{theorem}{Theorem}
|
|
|
|
\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}
|