\documentclass{article} \usepackage{amssymb} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %TCIDATA{OutputFilter=LATEX.DLL} %TCIDATA{Created=Monday, June 25, 2001 17:45:57} %TCIDATA{LastRevised=Saturday, June 01, 2002 20:48:29} %TCIDATA{} %TCIDATA{} %TCIDATA{CSTFile=On line bluem.cst} %TCIDATA{PageSetup=72,72,72,72,0} %TCIDATA{AllPages= %H=36 %F=36,\PARA{038
\QTR{small}{Matematick\U{e1} anal\U{fd}za I online - D\U{f4}kazy\dotfill \thepage }} %} \newtheorem{theorem}{Theorem} \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} \newtheorem{conjecture}[theorem]{Conjecture} \newtheorem{corollary}[theorem]{Corollary} \newtheorem{criterion}[theorem]{Criterion} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{exercise}[theorem]{Exercise} \newtheorem{lemma}[theorem]{Lemma} \newtheorem{notation}[theorem]{Notation} \newtheorem{problem}[theorem]{Problem} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{remark}[theorem]{Remark} \newtheorem{solution}[theorem]{Solution} \newtheorem{summary}[theorem]{Summary} \newenvironment{proof}[1][Proof]{\textbf{#1.} }{\ \rule{0.5em}{0.5em}} \input{tcilatex} \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 vety} \textbf{D\^{o}kaz: }Nech \[ p_{n}=\left\{ \begin{tabular}{ccc} $a_{n}$ & ak & $a_{n}\geq 0$ \\ $0$ & ak & $a_{n}<0$% \end{tabular}% \right. \;a\;q_{n}=\left\{ \begin{tabular}{ccc} $0$ & ak & $a_{n}\geq 0$ \\ $-a_{n}$ & ak & $a_{n}<0$% \end{tabular}% \right. . \]% Potom $a_{n}=p_{n}-q_{n}$. \v{D}alej vid\'{\i}me, \v{z}e $0\leq p_{n}\leq \left| a_{n}\right| $ \ aj $\ 0\leq q_{n}\leq \left| a_{n}\right| ,\,\forall n\in \mathbf{N}.$ Pod\v{l}a predpokladu rad $\sum_{n=1}^{\infty }\left| a_{n}\right| $ konverguje, potom pod\v{l}a porovn\'{a}vacieho krit\'{e}ria aj rady $\sum_{n=1}^{\infty }p_{n}$ a $\sum_{n=1}^{\infty }q_{n}$ konverguj% \'{u}. Tak konverguje aj rad $\sum_{n=1}^{\infty }\left( p_{n}-q_{n}\right) =\sum_{n=1}^{\infty }a_{n}.\blacksquare $ \begin{center} \begin{tabular}{|c|} \hline \hyperref{{\small Sp\"{a}\v{t}}}{}{}{M104.tex#2} \\ \hline \end{tabular} \end{center} \end{document}