How to get rid of the extra space above multline?

Question

By setting abovedisplayskip and belowdisplayskip I can shrink the vertical space before and after displayed equations. (How to globally change the spacing around equations?) However, multline seems to have some extra space that I can't get rid of. How to control this (ever so slight) gap?

\documentclass{article}
\usepackage{mathtools}

\begin{document}
\setlength\abovedisplayskip{0pt plus 2pt minus 3pt}
\setlength\belowdisplayskip{0pt plus 2pt minus 3pt}

\noindent
Lorem ipsum dolor sit amet, consectetur adipiscing
elit. \texttt{equation*}:
\begin{equation*}
  \begin{aligned}
  \smash{\Big|} a_{n+1} &= [2(n+1)][(n+1)^2-1]^{-1}
   = n^{-1} + (n+2)^{-1}
   \\
   &< (n-1)^{-1} + (n+1)^{-1}
   = (2n)(n^2 - 1)^{-1} = a_n.
  \end{aligned}
\end{equation*}
Lorem ipsum dolor sit amet, consectetur adipiscing
elit. \texttt{multline*}:
\begin{multline*}
 \smash{\Big|} a_{n+1} = [2(n+1)][(n+1)^2-1]^{-1}
 = n^{-1} + (n+2)^{-1}
 \\
 < (n-1)^{-1} + (n+1)^{-1}
 = (2n)(n^2 - 1)^{-1} = a_n.
\end{multline*}
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
\end{document}

Edit 1: Changed the MWE to something more realistic. Edit 2: Rewrote fractions to something not tall.

Answer 1

Both \begin{equation*}\begin{aligned}...\end{aligned}\end{equation*} and \begin{multline*}...\end{multline*} create display whose first line contains very tall items. This means that the normal \baselineskip is not used. Instead, \lineskip is used in addition to \abovedisplayskip.

In the former display, \lineskip is 1pt; in the latter display, \lineskip is increased to 4pt (the net increase of 3pt comes from \jot). If you want to cancel this net increase, you can say:

Lorem ipsum dolor sit amet, consectetur adipiscing
elit. \texttt{multline*}:% <- notice this comment sign here
\vadjust{\penalty\predisplaypenalty\vskip-\jot\relax}% <- magic!
\begin{multline*}
  \smash{\Bigg|} a_{n+1} = \frac{2(n+1)}{(n+1)^2-1}
  = \frac{1}{n} + \frac{1}{n+2}
  \\
  < \frac{1}{n-1} + \frac{1}{n+1}
  = \frac{2n}{n^2 - 1} = a_n.
\end{multline*}