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Enrique Andrade Gonzalez 2017-12-05 22:34:10 +00:00
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commit c43a36b693
1 changed files with 17 additions and 18 deletions
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33
03/solutions #3/solution #03.tex
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@ -17,14 +17,15 @@
\item Properly typeset the following command and properly refere to it in the text \item Properly typeset the following command and properly refere to it in the text
\begin{align} \begin{align}
(\sum_{i_1,\dots,i_m} a_{i_1,\dots,i_m} ^{2m}{m+1} ^{\frac{m+1}{2m}} \leq C\le \\ (\sum_{i_1,\dots,i_m} a_{i_1,\dots,i_m} ^{2m}(m+1) ^{\frac{m+1}{2m}}) \leq C\le \\
\sup\{ |\sum_{i_1,\dots, i_m} a_{i_1,\dots,i_m} x^1_{i_1}\dots x^m_{i_m}|: \|(x_i^k)_{i=1}^n \|_\infty\leq1,\ 1\leq k\leq m\}, \sup \left\{ \left\|\sum_{i_1,\dots, i_m} a_{i_1,\dots,i_m} x^1_{i_1}\dots x^m_{i_m}\right\|: \|(x_i^k)_{i=1}^n \|_\infty\leq1,\ 1\leq k\leq m\right\},
\end{align} \end{align}
%---------------------------------------------------------------------------------------------- %----------------------------------------------------------------------------------------------
% ¿Es correcto? % ¿Es correcto?
% ¿Is good? % ¿Is good?
\item Properly typset the expression: \[R \in z\] \item Properly typset the expression: \[
\operatorname{Re} z\]
@ -45,20 +46,20 @@ k=2\end{subarray}}^\infty a_n^k
%---------------------------------------------------------------------------------------------- %----------------------------------------------------------------------------------------------
% ¿Es correcto? % ¿Es correcto?
% ¿Is good? % ¿Is good?
\begin{theorem} \begin{theorem}[Cauchy--Hadamard] The radius of convergence $R$ of the power series
(Cauchy--Hadamard) \emph{The radius of convergence $R$ of the power series
\[ \[
\sum_{n=0}^\infty a_n(z-z_0)^n\ \ \ \ \ |z-z_0|<R \sum_{n=0}^\infty a_n(z-z_0)^n\quad |z-z_0|<R
\] \]
can by calculated via the following formula can by calculated via the following formula
\[ \[
\frac{1}{R}=limsup_{n\to\infty} \sqrt[n]{|a_n|}. \frac{1}{R}=\limsup_{n\to\infty} \sqrt[n]{|a_n|}.
\]} \]
\begin{defn}
(Prime numbers) A number is called prime, if it is not compound.
\end{defn}
\end{theorem} \end{theorem}
\begin{defn}[Prime numbers]
A number is called prime, if it is not compound.
\end{defn}
%---------------------------------------------------------------------------------------------- %----------------------------------------------------------------------------------------------
@ -67,15 +68,14 @@ can by calculated via the following formula
\item Typeset the follwing matrix (display-style): \item Typeset the follwing matrix (display-style):
\[ \[
\left\{\begin{array}{cc} \begin{pmatrix}
a_{11} & a_{12}\\ a_{11} & a_{12}\\
a_{21} & a_{22} a_{21} & a_{22}
\end{array} \end{pmatrix}
\right\} \]
\]
and in the text and in the text
$ $
\left(\begin{smallmatrix}{cc} \left(\begin{smallmatrix}
a_{11} & a_{12}\\ a_{11} & a_{12}\\
a_{21} & a_{22} a_{21} & a_{22}
\end{smallmatrix}\right) \end{smallmatrix}\right)
@ -89,4 +89,3 @@ $ Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do
\end{enumerate} \end{enumerate}
\end{document} \end{document}