27 lines
506 B
TeX
27 lines
506 B
TeX
\documentclass{article}
|
|
|
|
\input{../../../preamble}
|
|
|
|
\newcommand{\link}[1]{\lean{../../..}
|
|
{Common/Real/Sequence/Arithmetic}
|
|
{Real.Arithmetic.#1}
|
|
{Real.Arithmetic.#1}
|
|
}
|
|
|
|
\begin{document}
|
|
|
|
\section*{Sum of Arithmetic Series}%
|
|
\label{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}
|