2023-05-06 18:34:05 +00:00
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\documentclass{article}
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2023-05-07 21:57:40 +00:00
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\input{../../../preamble}
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2023-05-06 18:34:05 +00:00
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2023-05-11 02:19:18 +00:00
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\newcommand{\lean}[1]{\leanref
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2023-05-11 00:26:01 +00:00
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{./Geometric.html\#Real.Geometric.#1}
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{Real.Geometric.#1}}
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2023-05-06 18:34:05 +00:00
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\begin{document}
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2023-05-13 00:29:02 +00:00
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\section{\unverified{Sum of Geometric Series}}%
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2023-05-11 02:27:46 +00:00
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\label{sec:sum-geometric-series}
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2023-05-06 18:34:05 +00:00
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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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\begin{proof}
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2023-05-11 00:26:01 +00:00
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\lean{sum\_recursive\_closed}
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2023-05-06 18:34:05 +00:00
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\end{proof}
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\end{document}
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