This is what I have so far. The vertical dots go beyond the two edges. I want them to end before they reach them.
\documentclass[fleqn]{article}
\usepackage{amsmath,amsthm,amssymb,amsfonts}
\usepackage{tikz}
\usepackage{cancel}
\usepackage{color}
\usepackage{polynom}
\usepackage{graphicx}
\usepackage{fouriernc}
\usepackage[T1]{fontenc}
\usepackage{fancyhdr}
\pagestyle{fancy}
\usepackage{listing}
\usepackage{qtree}% For drawing trees.
\usepackage{pstricks,pst-node,pst-tree,pstricks-add}%This might be better.
\title{Trees}
\author{G}
\date{\today}
\begin{document}
\maketitle
{\pstree[treemode=R,levelsep=3.5]{\Tdot*[name=A] \taput{$\emptyset$}}{
\pstree[treemode=R, levelsep=3.5]{\Tdot*[name=B]\taput{$p_{1}$}}{%
{\pstree[treemode=R,levelsep=3.5]{\Tdot*[name=C]\taput{$p_{1}$}}% %
{\Tdot*[name=D]~{\dots}\taput{$p_{1}$} \Tdot*[name=E]~{\dots}\tbput{$p_{2}$}}}
{\pstree[treemode=R,levelsep=3.5]{\Tdot*[name=F]\tbput{$p_{2}$}}% %
{\Tdot*[name=G]~{\dots}\taput{$p_{1}$} \Tdot*[name=H]~{\dots}\tbput{$p_{2}$}}}}
\pstree[treemode=R, levelsep=3.5]{\Tdot*[name=I]\tbput{$p_{2}$}}{%\vdots
{\pstree[treemode=R,levelsep=3.5]{\Tdot*[name=J]\taput{$p_{1}$}}% %
{\Tdot*[name=K]~{\dots}\taput{$p_{1}$} \Tdot*[name=L]~{\dots}\tbput{$p_{2}$}}}
{\pstree[treemode=R,levelsep=3.5]{\Tdot*[name=M]\tbput{$p_{2}$}}% %
{\Tdot*[name=N]~{\dots}\taput{$p_{1}$} \Tdot*[name=P]~{\dots}\tbput{$p_{2}$}}}}
}}
\ncline[linestyle=dotted,nodesep=1.5mm,offset=1cm]{I}{B}
\end{document}

