How to align a single long equation split into multiple lines?

Question

I have a long equation that I need to wrap into multiple lines. I want to know what is the idiomatic way to align the multiple lines. I made two attempts at it and the results do not look good.

Example 1

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
  \frac{100 (100 + 1)}{2}
    & = 1 + 2 + 3 + 4 + 5 \\
    & + 6 + 7 + 8 + 9 + 10 \\
    & \vdots \\
    & + 96 + 97 + 98 + 99 + 100.  
\end{align*}
\end{document}

Here is the output:

Here all the + signs are aligned with = sign and that of course does not look good. In most mathematics books I see that the + sign is aligned with the first expression after the = sign, i.e., 1 in this case. So I made another attempt at it shown in the next example.

Example 2

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
  \frac{100 (100 + 1)}{2}
  = & 1 + 2 + 3 + 4 + 5 \\
    & + 6 + 7 + 8 + 9 + 10 \\
    & \vdots \\
    & + 96 + 97 + 98 + 99 + 100.  
\end{align*}
\end{document}

Here is the output:

This is closer to what I find in mathematics books but this is far from perfect. The = sign is sticking too close to the 1 after it. The \vdots appears misaligned.

I am wondering if there is an idiomatic way to typeset something like this in LaTeX? If yes, I would like to learn about it and use that.

Answer 1

\documentclass[preview,border=12pt,12pt]{standalone}
\usepackage{mathtools}

\begin{document}
\begin{align*}
\frac{100 (100 + 1)}{2} 
    &= \begin{aligned}[t]    
                1 
                &+ 2 + 3 + 4 + 5 \\
                &+ 6 + 7 + 8 + 9 + 10 \\
                &\,\;\vdots \\
                &+ 95 + 96 + 97 + 98 + 99 + 100
        \end{aligned}\\
    &= 5050
\end{align*}
\end{document}

Edit

And don't forget to follow the suggestion of Mico below:

Do consider replacing \,\;\vdots with \shortvdotswithin{+}.

Answer 2

The alignment point needn't be at =.

\documentclass{article}
\usepackage{amsmath,mathtools}

\begin{document}

\begin{equation*}
\mathtoolsset{shortvdotsadjustabove=3pt,shortvdotsadjustbelow=-1pt}
\begin{split}
  \frac{100 (100 + 1)}{2} =
    1 &+ 2 + 3 + 4 + 5 \\
      &+ 6 + 7 + 8 + 9 + 10 \\
      & \shortvdotswithin{+}
      &+ 95 + 96 + 97 + 98 + 99 + 100.
\end{split}
\end{equation*}

\end{document}

Answer 3

One of the following two solutions should be ok. They both use \vdotswithin rather than \vdots, to align the vertical dots on the + symbols. They differ in how the right-hand side of the first row is aligned relative to the right-hand side of the second row.

\documentclass{article}
\usepackage{mathtools} % for \vdotswithin macro
\begin{document}

\begin{align*}
  \frac{100 (100 + 1)}{2}
    & = 1 + 2 + 3 + 4 + 5 \\
    &\quad + 6 + 7 + 8 + 9 + 10 \\
    &\quad \vdotswithin{+} \\
    &\quad + 95 + 96 + 97 + 98 + 99 + 100.  
\end{align*}

\begin{align*}
  \frac{100 (100 + 1)}{2} =
    & \hphantom{{}+{}}1 + 2 + 3 + 4 + 5 \\
    & + 6 + 7 + 8 + 9 + 10 \\
    & \vdotswithin{+} \\
    & + 95 + 96 + 97 + 98 + 99 + 100.  
\end{align*}

\end{document}