bookshelf/common/Common/Sequence/Arithmetic.tex

\documentclass{article}

\input{../../preamble}

\begin{document}

\begin{theorem}[Sum of Arithmetic Series]

Let $(a_i)_{i \geq 0}$ be an arithmetic sequence with common difference $d$.
Then for some $n \in \mathbb{N}$,
$$\sum_{i=0}^n a_i = \frac{(n + 1)(a_0 + a_n)}{2}.$$

\end{theorem}

\begin{proof}

\href{Arithmetic.lean}{Common.Sequence.Arithmetic.sum_recursive_closed}

\end{proof}

\end{document}