f=Sin[x] Exp[-x]

Plot[f,{x,-1,6}]

s=Series[f,{x,0,8}]

ns=Normal[s]

Plot[ns,{x,-1,6}]

Plot[ns,{x,-1,6},PlotRange->{-0.5,0.5}]

Plot[{f,ns},{x,-1,6},PlotStyle->{Blue,Red},PlotRange->{-0.5,0.5}]

Manipulate[f=Sin[x] Exp[-x];s=Series[f,{x,0,n}];ns=Normal[s];
Plot[{f,ns},{x,-1,6},PlotStyle->{Blue,Red},PlotRange->{-0.5,0.5},PlotLabel->s],{n,0,15,1}]