CFe[r_, s_, f_] := 
      Drop[ContinuedFraction[E + r, f], s - 1]

"n=fraction denom, s=start coeff, f=finish coeff, pts=point size \
(fraction of graph size)";

n = 5; s = 1700; f = 2500; pts = 250;
$Line = 1; 
    Do[e[n, i] = 
        ListPlot[CFe[i/n, s, f], PlotRange -> All, 
          PlotStyle -> Hue[i/(n - 1)], 
          Prolog -> PointSize[1/200]], {i, 1, n - 1}];

Show[
        Graphics[
          Table[Rectangle[{0, 0}, {1, 2}, e[n, i]], {i, 1, 
              n - 1}]]];

"Note: for the combo to work, the range needs to be the same on all \
the graphs! If needed, adjust PlotRange manually using:"

MaxRange = Floor[1.1 Max[CFe[1/n, s, f]]]

"(Write PlotRange->{0,MaxRange} instead of PlotRange->All)"