bookshelf/Common/Real/Sequence/Arithmetic.tex

25 lines
493 B
TeX

\documentclass{article}
\input{../../../preamble}
\newcommand{\lean}[1]{\leanref
{./Arithmetic.html\#Real.Arithmetic.#1}
{Real.Arithmetic.#1}}
\begin{document}
\section{\proceeding{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}
\lean{sum\_recursive\_closed}
\end{proof}
\end{document}