bookshelf/Common/Real/Sequence/Arithmetic.tex

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\documentclass{article}
2023-05-07 21:57:40 +00:00
\input{../../../preamble}
\newcommand{\link}[1]{\lean{../../..}
{Common/Real/Sequence/Arithmetic} % Location
{Real.Arithmetic.#1} % Namespace
{Real.Arithmetic.#1} % Presentation
}
\begin{document}
\section{\proceeding{Sum of Arithmetic Series}}%
\hyperlabel{sec:sum-arithmetic-series}%
Let $(a_i)_{i \geq 0}$ be an arithmetic sequence with common difference $d$.
Then for some $n \in \mathbb{N}$,
$$\sum_{i=0}^n a_i = \frac{(n + 1)(a_0 + a_n)}{2}.$$
\begin{proof}
\link{sum\_recursive\_closed}
\end{proof}
\end{document}