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\QTR{small}{Matematick\U{e1} anal\U{fd}za I online - D\U{f4}kazy\dotfill \thepage }}
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\begin{document}
\author{A. U. Thor}
\title{Lab Report}
\date{The Date }
\maketitle
\begin{abstract}
A Laboratory report created with Scientific Notebook
\end{abstract}
\section{Postupnosti a rady re\'{a}lnych \v{c}\'{\i}sel}
\subsection{D\^{o}kaz}
\textbf{D\^{o}kaz: }a) Nech $\left| x-a\right| <\left| c-a\right| $, potom%
\[
\sum_{n=0}^{\infty }c_{n}\left( x-a\right) ^{n}=\sum_{n=0}^{\infty
}c_{n}\left( c-a\right) ^{n}\left( \frac{x-a}{c-a}\right) ^{n}.
\]%
Preto\v{z}e $\sum_{n=0}^{\infty }c_{n}\left( c-a\right) ^{n}$ konverguje,
plat\'{\i} $\lim_{n\longrightarrow \infty }c_{n}\left( c-a\right) ^{n}=0$,
teda $\exists n_{0}:\forall n\geq n_{0}\;\left| c_{n}\left( c-a\right)
^{n}\right|