Ramp-Like Function

  part1=Plot[0,{x,-2,0},DisplayFunction->Identity];
  part2=Plot[2-x,{x,0,2},DisplayFunction->Identity];
  graph=Show[part1,part2,
  DisplayFunction->$DisplayFunction,AspectRatio->Automatic];

  Clear[a0,a,b,c,Sn]
  a0=(1/4)(Integrate[0,{x,-2,0}]+Integrate[2-x,{x,0,2}]);
  a0

  a[n_]:=a[n]=(1/2)(Integrate[0 Cos[n Pi x/2],{x,-2,0}]+
  Integrate[(2-x) Cos[n Pi x/2],{x,0,2}]);
  Table[a[n],{n,1,5}]

  b[n_]:=b[n]=(1/2)(Integrate[0 Sin[n Pi x/2],{x,-2,0}]+
  Integrate[(2-x) Sin[n Pi x/2],{x,0,2}]);
  Table[b[n],{n,1,5}]

  Sn=a0+Sum[a[n]Cos[n Pi x/2]+b[n]Sin[n Pi x/2],{n,1,5}]

  p3=Plot[Sn,{x,-2,2}];

  Show[graph,p3];

  Clear[c]

  c[n_]:=c[n]=(1/4)(Integrate[0 Exp[- I n Pi x/2],{x,-2,0}]+
  Integrate[(2-x) Exp[- I n Pi x/2],{x,0,2}]);
  Table[c[n],{n,-5,5}]

  ISn=Sum[c[n]Exp[I n Pi x/2],{n,-5,5}];

  ComplexExpand[ISn]

  p4=Plot[ISn,{x,-2,2}];

  Show[graph,p4];

  Sn
  ComplexExpand[ISn]

  Simplify[Sn-ISn]

Up to Examples Using Complex Fourier Series