Taylor Series

p1=Plot[Sin[z]Exp[-z],{z,0,5},PlotStyle->{Thickness[0.02],Opacity[0.5]}];
p2=Plot[Evaluate[Table[Normal[Series[Sin[z]Exp[-z],
{z,0,n}]],{n,1,24}]],{z, 0,5},PlotStyle->"BrightBands"];
Show[p1,p2,ImageSize->Large]