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\section{Section one}
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\begin{definition}
Given an infinite sequence $\{x_k\}_{k \in \mathbb{N}}$, the $kth$ partial sum $S_k$ is the sum of the first $k$ terms of the sequence, that is, $$S_k = \sum_{n = 1}^{k} x_n.$$
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\begin{definition}
A series converges if $\exists L \in \mathbb{R}$ such that $\forall \varepsilon \in \mathbb{R}, \varepsilon > 0, \exists N \in \mathbb{N}$ (sufficiently large) such that $\forall n \geq N$, $$\vert S_n - L \vert < \varepsilon.$$
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\section{References}
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\bibitem{manfredo}
~DO CARMO, M. P., \emph{Differential Geometry of Curves and Surfaces}, Rio de Janeiro: Instituto de Matemática Pura e Aplicada (IMPA), 1976.
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