27 lines
506 B
TeX
27 lines
506 B
TeX
\documentclass{article}
|
|
|
|
\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}
|