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Catarina Gamelas 2018-10-23 18:18:47 +02:00
parent d30e11af69
commit 42e737b9da
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exercise-02-plik.pdf
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exercise-02-plik.tex
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@ -3,7 +3,7 @@
\usepackage{polski}
\usepackage{amsmath}
\newtheorem{thm}{Theorem}
\newtheorem{df}{Defenition}
\newtheorem{df}{defenition}
\begin{document}
\begin{enumerate}
@ -24,14 +24,14 @@ f(x)=\sum_{\substack{n=0\\ k=2}}^\infty a_n^k
\item Properly typeset the following theorem
\begin{thm}[Cauchy--Hadamard]
\noindent\textbf{Theorem 1} (Cauchy--Hadamard) \emph{The radius of convergence $R$ of the power series
The radius of convergence $R$ of the power series
\[
\sum_{n=0}^\infty a_n(z-z_0)^n\ \ \ \ \ |z-z_0|<R
\]
can by calculated via the following formula
\[
\frac{1}{R}=\limsup_{n\to\infty} \sqrt[n]{|a_n|}.
\]}
\]
\end{thm}