f=1/(1-x);a=0;n=6;nmax=10;
Print[Series[f,{x,a,nmax}]];
Manipulate[
Plot[{f,Normal[Evaluate[Series[f,{x,a,n}]]]}/.{x->q},{q,-3,3},PlotRange->{-10,10},PlotLabel->Normal[Evaluate[Series[f,{x,a,n}]]]],{n,0,nmax,1}]