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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2023-05-03 19:09:58 +00:00
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\newcommand{\link}[1]{\lean{../../..}
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2023-05-10 16:45:42 +00:00
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{Common/Real/Sequence/Arithmetic} % Location
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{Real.Arithmetic.#1} % Namespace
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{Real.Arithmetic.#1} % Presentation
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2023-05-03 19:09:58 +00:00
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}
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\begin{document}
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2023-05-10 16:45:42 +00:00
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\section{\proceeding{Sum of Arithmetic Series}}%
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\hyperlabel{sec:sum-arithmetic-series}%
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2023-05-06 18:34:05 +00:00
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Let $(a_i)_{i \geq 0}$ be an arithmetic sequence with common difference $d$.
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Then for some $n \in \mathbb{N}$,
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$$\sum_{i=0}^n a_i = \frac{(n + 1)(a_0 + a_n)}{2}.$$
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\begin{proof}
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2023-05-03 19:09:58 +00:00
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\link{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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