a = 10
f1[x_] := 
        (1/3) + (∑_(n = 1)^a) (4/((n^2)*(π^2)))*(((-1))^n)*
              Cos[n*π*x];
g1[x_] := (x^2);
h1[x_] := (x^2) - (1/3);
k1[
          x_] := (∑_(n = 1)^a) (4/((n^2)*(π^2)))*(((-1))^n)*
            Cos[n*π*x];
R1 = 
      Plot[f1[x], {x, -2, 2}, 
        PlotStyle -> {RGBColor[1, 0.5, 0], Thickness[0.005]}, 
        AspectRatio -> Automatic]
L1 = 
      Plot[g1[x], {x, -2, 2}, 
        PlotStyle -> {RGBColor[0.5, 0.5, 0], Thickness[0.01]}, 
        AspectRatio -> Automatic]
Show[L1, R1]
H1 = 
      Plot[h1[x], {x, -2, 2}, 
        PlotStyle -> {RGBColor[0.5, 1, 0], Thickness[0.01]}, 
        AspectRatio -> Automatic]
K1 = 
      Plot[k1[x], {x, -2, 2}, 
        PlotStyle -> {RGBColor[0.1, 0.5, 0.5], Thickness[0.005]}, 
        AspectRatio -> Automatic]
Show[H1, K1]

a = 10
f2[
          x_] := (1/3) 
            x + (∑_(n = 1)^a) (4/((n^2)*(π^2)))*(((-1))^n)*(1/(n*π))*Sin[n*π*x] + 0;
g2[x_] := (1/3) (x^3);
h2[x_] := (1/3) (x^3) - (1/3) x;
k2[
          x_] := (∑_(n = 1)^a) (4/((n^2)*(π^2)))*(((-1))^n)*(1/(n*π))*
            Sin[n*π*x];
R2 = 
      Plot[f2[x], {x, -2, 2}, 
        PlotStyle -> {RGBColor[1, 0.5, 0], Thickness[0.005]}, 
        AspectRatio -> Automatic]
L2 = 
      Plot[g2[x], {x, -2, 2}, PlotRange -> {-1, 1}, 
        PlotStyle -> {RGBColor[0.5, 0.5, 0], Thickness[0.01]}, 
        AspectRatio -> Automatic]
Show[L2, R2]
H2 = 
      Plot[h2[x], {x, -2, 2}, 
        PlotStyle -> {RGBColor[0.5, 1, 0], Thickness[0.01]}, 
        AspectRatio -> Automatic]
K2 = 
      Plot[k2[x], {x, -2, 2}, 
        PlotStyle -> {RGBColor[0.1, 0.5, 0.5], Thickness[0.005]}, 
        AspectRatio -> 1/5]
Show[H2, K2]

a = 10
f3[
          x_] := (1/6) 
            (x^2) + (∑_(n = 1)^a) (4/((n^2)*(π^2)))*(((-1))^n)*(1/(n*π))*((-1)/(n*π))*
              Cos[n*π*x] - (7/180);
g3[x_] := (1/12) (x^4);
h3[
          x_] := (1/12) (x^4) - (1/6) (x^2);
k3[
          x_] := (∑_(n = 1)^a) (4/((n^2)*(π^2)))*(((-1))^n)*(1/(n*π))*((-1)/(n*π))*
              Cos[n*π*x] - (7/180);
R3 = 
      Plot[f3[x], {x, -2, 2}, PlotRange -> {-0.5, 0.5}, 
        PlotStyle -> {RGBColor[1, 0.5, 0], Thickness[0.005]}, 
        AspectRatio -> Automatic]
L3 = 
      Plot[g3[x], {x, -2, 2}, PlotRange -> {-1, 1}, 
        PlotStyle -> {RGBColor[0.5, 0.5, 0], Thickness[0.01]}, 
        AspectRatio -> Automatic]
Show[L3, R3]
H3 = 
      Plot[h3[x], {x, -2, 2}, 
        PlotStyle -> {RGBColor[0.5, 1, 0], Thickness[0.01]}, 
        AspectRatio -> 1/10]
K3 = 
      Plot[k3[x], {x, -2, 2}, 
        PlotStyle -> {RGBColor[0.1, 0.5, 0.5], Thickness[0.005]}, 
        AspectRatio -> (1/4)]
Show[H3, K3]

a = 10
f4[
          x_] := (1/18) 
            (x^3) + (∑_(n = 1)^a) (4/((n^2)*(π^2)))*(((-1))^n)*((-1)/((n^2)*(π^2)))*(1/(n*π))*Sin[n*π*x] - (7/180) 
            x;
g4[x_] := (1/60) (x^5);
h4[
          x_] := (1/60) (x^5) - (1/18) (x^3) + (7/180) 
            x;
k4[
          x_] := (∑_(n = 1)^a) (4/((n^2)*(π^2)))*(((-1))^n)*((-1)/((n^2)*(π^2)))*(1/(n*π))*
            Sin[n*π*x];
R4 = 
      Plot[f4[x], {x, -2, 2}, PlotRange -> {-0.5, 0.5}, 
        PlotStyle -> {RGBColor[1, 0.5, 0], Thickness[0.005]}, 
        AspectRatio -> 1/2]
L4 = 
      Plot[g4[x], {x, -2, 2}, PlotRange -> {-0.5, 0.5}, 
        PlotStyle -> {RGBColor[0.5, 0.5, 0], Thickness[0.01]}, 
        AspectRatio -> 1/3]
Show[L4, R4]
H4 = 
      Plot[h4[x], {x, -2, 2}, 
        PlotStyle -> {RGBColor[0.5, 1, 0], Thickness[0.01]}, 
        AspectRatio -> 1/5]
K4 = 
      Plot[k4[x], {x, -2, 2}, 
        PlotStyle -> {RGBColor[0.1, 0.5, 0.5], Thickness[0.005]}, 
        AspectRatio -> 1/5]
Show[H4, K4]