bookshelf/common/Common/Sequence/Geometric.tex

\documentclass{article}

\input{../../preamble}

\begin{document}

\begin{theorem}[Sum of Geometric Series]

Let $(a_i)_{i \geq 0}$ be a geometric sequence with common ratio $r \neq 1$.
Then for some $n \in \mathbb{N}$,
$$\sum_{i=0}^n a_i = \frac{a_0(1 - r^{n+1})}{1 - r}.$$

\end{theorem}

\begin{proof}

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

\end{proof}

\end{document}