Series[(1 + x)^(1/3), {x, 0, 3}]

powthirdseries = 
      Normal[Series[(1 + x)^(1/3), {x, 0, 3}]]

Plot[{powthirdseries, (1 + x)^(1/3)}, {x, -1, 1.1}, 
      PlotStyle -> {RGBColor[1, 0, 0], RGBColor[0, 0, 1]}]

Plot[1/x^2 - 2/x, {x, 0.25, 4}]

potseries = Normal[Series[1/x^2 - 2/x, {x, 1, 2}]]

Plot[{potseries, 1/x^2 - 2/x}, {x, 0.25, 4}, 
      PlotStyle -> {RGBColor[1, 0, 0], RGBColor[0, 0, 1]}]