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

nmax = 75;
Do[
Print["n=", n]; 
Plot[
          Evaluate[{Exp[x], Normal[Series[Exp[x], {x, 0, n}]]}], {x, -50, 
            5}, PlotRange -> {0, 10}];
, {n, 0, 
          nmax}];