29 lines
599 B
TeX
29 lines
599 B
TeX
\documentclass{article}
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\usepackage{amsfonts, amsthm}
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\usepackage{hyperref}
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\newtheorem{theorem}{Theorem}
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\newtheorem{custominner}{Theorem}
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\newenvironment{custom}[1]{%
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\renewcommand\thecustominner{#1}%
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\custominner
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}{\endcustominner}
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\begin{document}
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\begin{theorem}[Sum of Geometric Series]
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Let $(a_i)_{i \geq 0}$ be a geometric sequence with common ratio $r \neq 1$.
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Then for some $n \in \mathbb{N}$,
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$$\sum_{i=0}^n a_i = \frac{a_0(1 - r^{n+1})}{1 - r}.$$
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\end{theorem}
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\begin{proof}
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\href{Geometric.lean}{Common.Sequence.Geometric.sum\_recursive\_closed}
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\end{proof}
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\end{document}
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