fs:=x->(2*L/Pi)*(sin(Pi*x/L)-1/2*sin(2*Pi*x/L)+(1/3)*sin(3*Pi*x/L));

L:=Pi;

plot(fs(x), x=-3*Pi..3*Pi);

fs:=x->(2*L/Pi)*(sin(Pi*x/L)-1/2*sin(2*Pi*x/L)+(1/3)*sin(3*Pi*x/L)-1/4*sin(4*Pi*x/L));

plot(fs(x), x=-3*Pi..3*Pi);

fs:=x->(2*L/Pi)*(sin(Pi*x/L)-1/2*sin(2*Pi*x/L)+(1/3)*sin(3*Pi*x/L)-1/4*sin(4*Pi*x/L+1/5*sin(5*Pi*x/L)));

plot(fs(x), x=-3*Pi..3*Pi);

fs:=x->(2*L/Pi)*(sin(Pi*x/L)-1/2*sin(2*Pi*x/L)+(1/3)*sin(3*Pi*x/L)-1/4*sin(4*Pi*x/L)+1/5*sin(5*Pi*x/L)-1/6*sin(6*Pi*x/L));

plot(fs(x), x=-3*Pi..3*Pi);

fs:=x->(2*L/Pi)*(sin(Pi*x/L)-1/2*sin(2*Pi*x/L)+(1/3)*sin(3*Pi*x/L)-1/4*sin(4*Pi*x/L)+1/5*sin(5*Pi*x/L)-1/6*sin(6*Pi*x/L)+1/7*sin(7*Pi*x/L)-1/8*sin(8*Pi*x/L));

plot(fs(x), x=-3*Pi..3*Pi);

restart;

L=Pi;

tot := 0: for i from 1 to 100 do tot :=tot + (-1)^(i+1)* (2*L/Pi)*((1/i)*sin(i*Pi*x/L));end do:

fs:=unapply(tot,x,L):

plot(fs(x,Pi), x=-3*Pi..3*Pi);

Another example

restart;

tot := 0: for i from 1 by 2 to 100 do tot :=tot + (400/Pi)*((1/i)*sin(i*Pi*x/L));end do:

fs:=unapply(tot,x,L):

plot(fs(x,1), x=-1..1);