27 lines
503 B
TeX
27 lines
503 B
TeX
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\documentclass{article}
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\input{../../../preamble}
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\newcommand{\link}[1]{\lean{../../..}
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{Common/Real/Sequence/Geometric}
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{Real.Geometric.#1}
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{Real.Geometric.#1}
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}
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\begin{document}
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\section*{Sum of Geometric Series}%
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\label{sec:sum-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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\begin{proof}
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\link{sum\_recursive\_closed}
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\end{proof}
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\end{document}
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