n = 6;
Series[1/x, {x, 2, 5}]

nmax = 50; inte = 2;
Do[
Print["n=", n]; 
Plot[
          Evaluate[{1/x, Normal[Series[1/x, {x, 2, n}]]}], {x, -6, 6}, 
          PlotRange -> {-12, 12}];
, {n, 0, 
          nmax}];