2023-05-06 18:34:05 +00:00
|
|
|
\documentclass{article}
|
|
|
|
|
|
2023-05-07 21:57:40 +00:00
|
|
|
\input{../../../preamble}
|
2023-05-06 18:34:05 +00:00
|
|
|
|
2023-05-11 02:19:18 +00:00
|
|
|
\newcommand{\lean}[1]{\leanref
|
2023-05-11 00:26:01 +00:00
|
|
|
{./Arithmetic.html\#Real.Arithmetic.#1}
|
|
|
|
|
{Real.Arithmetic.#1}}
|
2023-05-06 18:34:05 +00:00
|
|
|
|
|
|
|
|
\begin{document}
|
|
|
|
|
|
2023-05-13 00:29:02 +00:00
|
|
|
\section{\unverified{Sum of Arithmetic Series}}%
|
2023-05-11 02:27:46 +00:00
|
|
|
\label{sec:sum-arithmetic-series}
|
2023-05-06 18:34:05 +00:00
|
|
|
|
|
|
|
|
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}
|
|
|
|
|
|
2023-05-11 00:26:01 +00:00
|
|
|
\lean{sum\_recursive\_closed}
|
2023-05-06 18:34:05 +00:00
|
|
|
|
|
|
|
|
\end{proof}
|
|
|
|
|
|
|
|
|
|
\end{document}
|
