How to align equations not considering the document margins?

Question

I set the margins of the document but if I write a too long equation only using $$...$$, align*, or equation* and then aligned environments centers the equation, but from the left margin.

So the question is, How to center an equation considering only the width of the document, and not the margins?

Here is my MWE:

\documentclass{article}
\usepackage{amsmath}
\usepackage{vmargin}

\setpapersize{A4}
\setmargins{2.2cm}
{0.5cm}
{16.5cm}
{23.42cm}               
{30pt}
{1cm}
{0pt}
{2cm}   

\begin{document}

% With $$...$$ there is less spacing. I definitely do not want to use this option.
$$
a_n=\sqrt[n]{n}=1+h\Rightarrow n={(1+h)}^n\underbrace{=}_{\substack{\text{Por binomio de Newton}\\\text{(Ver \textbf{OBSERVACI\'ON})}}}1+nh+\dfrac{n(n-1)}{2!}h^2+\cdots +h^n\underbrace{\geq}_{\substack{\text{Como todos los sumandos son}\\\text{positivos, se puede acotar}\\\text{inferiormente con uno solo}\\\text{de ellos}}} \dfrac{n(n-1)}{2!}h^2.
$$

% With equation* and aligned environments space properly, but center from the left margin.
\begin{equation*}
    \begin{aligned}
        a_n=\sqrt[n]{n}=1+h\Rightarrow n={(1+h)}^n\underbrace{=}_{\substack{\text{Por binomio de Newton}\\\text{(Ver \textbf{OBSERVACI\'ON})}}}1+nh+\dfrac{n(n-1)}{2!}h^2+\cdots +h^n\underbrace{\geq}_{\substack{\text{Como todos los sumandos son}\\\text{positivos, se puede acotar}\\\text{inferiormente con uno solo}\\\text{de ellos}}} \dfrac{n(n-1)}{2!}h^2.
    \end{aligned}
\end{equation*}

% With align* environment it is the same as with equation* and aligned environments.
\begin{align*}
    a_n=\sqrt[n]{n}=1+h\Rightarrow n={(1+h)}^n\underbrace{=}_{\substack{\text{Por binomio de Newton}\\\text{(Ver \textbf{OBSERVACI\'ON})}}}1+nh+\dfrac{n(n-1)}{2!}h^2+\cdots +h^n\underbrace{\geq}_{\substack{\text{Como todos los sumandos son}\\\text{positivos, se puede acotar}\\\text{inferiormente con uno solo}\\\text{de ellos}}} \dfrac{n(n-1)}{2!}h^2.
\end{align*}

\end{document}

And the result is:

Thanks!

Answer 1

This doesn't directly address the margins issue, but to make the equation short enough to fit within your margins, you might consider using \mathclap from the mathtools package (which should be used instead of, not in addition to amsmath).

Note also that you should use \[..\] instead of $$..$$. Explanation here.

\documentclass{article}
\usepackage{mathtools}
\usepackage{vmargin}

\setpapersize{A4}
\setmargins{2.2cm}
{0.5cm}
{16.5cm}
{23.42cm}               
{30pt}
{1cm}
{0pt}
{2cm}   

\begin{document}

\[
a_n=\sqrt[n]{n}=1+h\Rightarrow n={(1+h)}^n\underbrace{=}_%
    {\mathclap{\substack{\text{Por binomio de Newton}\\\text{(Ver \textbf{OBSERVACI\'ON})}}}}%
    1+nh+\dfrac{n(n-1)}{2!}h^2+\cdots +h^n\underbrace{\geq}_%
    {\mathclap{\substack{\text{Como todos los sumandos son}\\\text{positivos, se puede acotar}\\\text{inferiormente con uno solo}\\\text{de ellos}}}}%
    \dfrac{n(n-1)}{2!}h^2.
\]

\end{document}

Answer 2

Setting text or equations in the margins is usually not the solution. Here I present a different way to display your argument.

Some important details: avoid vmargin, which is incompatible with several other packages, notably TikZ. The same settings can be more clearly obtained with geometry. The showframe option is just for drawing lines that illustrate the page setup. Remove it for the final version.

\documentclass{article}
\usepackage{amsmath}
\usepackage[
  showframe,
  a4paper,
  includehead,
  left=2.2cm,
  top=0.5cm,
  textwidth=16.5cm,
  textheight=23.42cm,
  heightrounded,
  headheight=30pt,
  headsep=1cm,
  footskip=2cm,
]{geometry}

\newcommand{\eqdesc}[1]{%
  \text{\footnotesize\begin{tabular}{@{}l@{}}#1\end{tabular}}%
}

\begin{document}

\begin{align*}
a_n=\sqrt[n]{n}=1+h
\implies
n &= (1+h)^n \\
  &= 1+nh+\frac{n(n-1)}{2!}h^2+\dots+h^n
&& \eqdesc{Por binomio de Newton\\(Ver \textbf{OBSERVACI\'ON})} \\
  &\geq \frac{n(n-1)}{2!}h^2.
&& \eqdesc{Como todos los sumandos son\\positivos, se puede acotar\\
           inferiormente con uno solo\\de ellos}
\end{align*}

\end{document}

Answer 3

It's not very tidy, and it's not automatic, but you could use "\hspace*" to force equations left. If there are multiple wide equations, all wide equations need this treatment. Experiment with the values till it looks OK.

\documentclass{article}
\usepackage{amsmath}
\usepackage{vmargin}

\setpapersize{A4}
\setmargins{2.2cm}
{0.5cm}
{16.5cm}
{23.42cm}               
{30pt}
{1cm}
{0pt}
{2cm}   

\begin{document}

% With $$...$$ there is less spacing. I definitely do not want to use this option.
$$
\hspace*{-8mm}
a_n=\sqrt[n]{n}=1+h\Rightarrow n={(1+h)}^n\underbrace{=}_{\substack{\text{Por binomio de Newton}\\\text{(Ver \textbf{OBSERVACI\'ON})}}}1+nh+\dfrac{n(n-1)}{2!}h^2+\cdots +h^n\underbrace{\geq}_{\substack{\text{Como todos los sumandos son}\\\text{positivos, se puede acotar}\\\text{inferiormente con uno solo}\\\text{de ellos}}} \dfrac{n(n-1)}{2!}h^2.
$$

% With equation* and aligned environments space properly, but center from the left margin.
\begin{equation*}
    \hspace*{-11mm}
    \begin{aligned}
        a_n=\sqrt[n]{n}=1+h\Rightarrow n={(1+h)}^n\underbrace{=}_{\substack{\text{Por binomio de Newton}\\\text{(Ver \textbf{OBSERVACI\'ON})}}}1+nh+\dfrac{n(n-1)}{2!}h^2+\cdots +h^n\underbrace{\geq}_{\substack{\text{Como todos los sumandos son}\\\text{positivos, se puede acotar}\\\text{inferiormente con uno solo}\\\text{de ellos}}} \dfrac{n(n-1)}{2!}h^2.
    \end{aligned}
\end{equation*}

% With align* environment it is the same as with equation* and aligned environments.
\begin{align*}
    \hspace*{-11mm}
    a_n=\sqrt[n]{n}=1+h\Rightarrow n={(1+h)}^n\underbrace{=}_{\substack{\text{Por binomio de Newton}\\\text{(Ver \textbf{OBSERVACI\'ON})}}}1+nh+\dfrac{n(n-1)}{2!}h^2+\cdots +h^n\underbrace{\geq}_{\substack{\text{Como todos los sumandos son}\\\text{positivos, se puede acotar}\\\text{inferiormente con uno solo}\\\text{de ellos}}} \dfrac{n(n-1)}{2!}h^2.
\end{align*}

\end{document}