x[n_]:=x[n]=If[n==0,0,(n+x[n-1])/(1-n*x[n-1])];

x1[n_]:=x1[n]=If[n==0,0,N[(n+x1[n-1])/(1-n*x1[n-1])]];

x[0]

x[1]

x[2]

Table[x[i],{i,0,20}]

Table[x1[i],{i,0,20}]

ListPlot[Table[x1[i],{i,0,500}]]

y[n_]:=y[n]=x[n]-Floor[x[n]];

Table[y[i],{i,0,10}]

y1[n_]:=y1[n]=x1[n]-Floor[x1[n]];

y1[500]

N[y[500]]

ListPlot[Table[y1[i],{i,0,50000}],PlotStyle->PointSize[.005]]

ListPlot[Table[y1[i],{i,0,100000,2}],PlotStyle->PointSize[.005]]