bookshelf/Common/Real/Sequence/Arithmetic.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}