How do you place texts "side by side"

Two side-by-side minipage environments will work. In the example below, the left-hand minipage is twice as wide as the one on the right; feel free to adjust the relative sizes to suit your needs.

\documentclass{article}
\usepackage{amsmath} % for "\text" macro
\begin{document}

\noindent
\begin{minipage}[t]{0.6667\textwidth}
\textbf{Root test}: 
Given $\displaystyle \sum_{n=1}^\infty \lvert a_n\rvert^{\frac{1}{n}}$ then:

\smallskip
1. $L>0 \Rightarrow \text{Divergent}$

2. $L<0 \Rightarrow \text{Convergent}$

3. $L=0 \text{ Undetermined}$
\end{minipage}% % leave no gap
\begin{minipage}[t]{0.3333\textwidth}
Divergent:

$\displaystyle \sum_{n=1}^\infty \frac{-12^n}{n}$

\bigskip
Convergent:

$\displaystyle \sum_{n=1}^\infty \frac{n^n}{3^{1+2n}}$
\end{minipage}

\end{document}

It's possible to use \parbox{...}{...}\hfill\parbox{...}{...} like in :

\documentclass{article}
\usepackage{amsmath}
\begin{document}

\parbox{0.6\textwidth}{
\textbf{Root test}: 
Given $\displaystyle \sum_{n=1}^\infty \lvert a_n\rvert^{\frac{1}{n}}$ then:

\smallskip
1. $L>0 \Rightarrow \text{Divergent}$

2. $L<0 \Rightarrow \text{Convergent}$

3. $L=0 \text{ Undetermined}$
}
\hfill
\parbox{0.3\textwidth}{
Divergent:

$\displaystyle \sum_{n=1}^\infty \frac{-12^n}{n}$

\bigskip
Convergent:

$\displaystyle \sum_{n=1}^\infty \frac{n^n}{3^{1+2n}}$
}

\end{document}