n = 6;
Series[Cos[x], {x, 0, n}]

nmax = 50; inte = 2;
Do[
Print["n=", n]; 
Plot[
          Evaluate[{Cos[x], 
              Normal[Series[Cos[x], {x, 0, n}]]}], {x, -inte 2  π, 
            inte 2  π}, 
          PlotRange -> {-2, 2}];
, {n, 0, 
          nmax}];