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\QTR{small}{Matematick\U{e1} anal\U{fd}za III online - D\U{f4}kazy\dotfill \thepage }}
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\newtheorem{acknowledgement}[theorem]{Acknowledgement}
\newtheorem{algorithm}[theorem]{Algorithm}
\newtheorem{axiom}[theorem]{Axiom}
\newtheorem{case}[theorem]{Case}
\newtheorem{claim}[theorem]{Claim}
\newtheorem{conclusion}[theorem]{Conclusion}
\newtheorem{condition}[theorem]{Condition}
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\newtheorem{corollary}[theorem]{Corollary}
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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{Komplexn\'{e} \v{c}\'{\i}sla a funkcie komplexnej premennej}
\subsection{D\^{o}kaz vety}
\textbf{D\^{o}kaz: }a) Pre
\[
\left| z-a\right| <\left| z_{0}-a\right| \Longrightarrow \left| \frac{z-a}{%
z_{0}-a}\right| <1.
\]%
Potom
\begin{equation}
\left| c_{n}(z-a)^{n}\right| =\left| c_{n}(z_{0}-a)^{n}\right| \left| \frac{%
z-a}{z_{0}-a}\right| ^{n}<\left| c_{n}(z_{0}-a)^{n}\right| \tag{(a)}
\end{equation}%
Pod\v{l}a predpokladu rad $\sum_{n=0}^{\infty }c_{n}\left( z_{0}-a\right)
^{n}$ konverguje, potom $\lim_{n\longrightarrow \infty }c_{n}\left(
z_{0}-a\right) ^{n}=0,$ \v{c}o implikuje, \v{z}e existuje $C>0$ tak\'{e},
\v{z}e
\[
\left| c_{n}(z_{0}-a)^{n}\right|