\begin{tikzpicture}
    \node[state] (1) at (0,0) {1};
    \node[state] (2) at (1.5,0) {2};
    \node[state] (3) at (3,0) {3};
    \node (4) at (4.5,0) {$\cdots$};
    \node[state] (n) at (6,0) {$n$};
    \node[state] (T) at (6,2) {T};
    \node (5) at (7.5,0) {$\cdots$};
    
   \path[->]
    (1) edge node [below] {$\frac{1}{2}$} (2)
    (1) edge node [] {$2$} (T);
   \path[->] 
    (2) edge node [below] {$\frac{1}{2}$} (3)
    (2) edge node [] {${2^3}$} (T);
   \path[->]  
    (3) edge node [below] {$\frac{1}{2}$} (4)
    (3) edge node [] {${2^3}$} (T);
   \path[->] 
    (4) edge node [below] {$\frac{1}{2}$} (n);
   \path[->] 
    (n) edge node [below] {$\frac{1}{2}$} (5)
    (n) edge node [] {${2^n}$} (T);
\end{tikzpicture}