Plot[Abs[x],{x,-1,1},PlotRange->{{-3,3},{-1,2}},AspectRatio->Automatic]

Plot[{Abs[x],Abs[x-Floor[((x-(-1))/(1-(-1)))](1-(-1))]},{x,-5,5},PlotRange->{{-3,3},{-1,2}},AspectRatio->Automatic]

(1/2)Integrate[Abs[x],{x,-1,1}]

(1/1)Integrate[Abs[x]Cos[((k Pi)/1) x],{x,-1,1}]

((2 (-1+Cos[k π]))/((k^2) (π^2)))

(1/2)+Sum[((2 (-1+Cos[k π]))/((k^2) (π^2)))Cos[k Pi x],{k,1,10}]

Plot[{Abs[x],Abs[x-Floor[((x-(-1))/(1-(-1)))](1-(-1))],(1/2)+Sum[((2 (-1+Cos[k π]))/((k^2) (π^2)))Cos[k Pi x],{k,1,5}]},{x,-5,5},PlotRange->{{-3,3},{-1,2}},AspectRatio->Automatic]

Plot[Mod[x-1,2,0],{x,-5,5},PlotRange->{{-3,3},{-1,2}},AspectRatio->Automatic]

Plot[{Abs[x],Abs[Mod[x,2,-1]],(1/2)+Sum[((2 (-1+Cos[k π]))/((k^2) (π^2)))Cos[k Pi x],{k,1,5}]},{x,-5,5},PlotRange->{{-3,3},{-1,2}},AspectRatio->Automatic]