clear;
clf();

lambda=10; %Wavelength
k=2*pi/lambda; %Wave number
x=0:0.01:40; %plot range

c0 = 1/2;%Y axis offset
f_x= c0/2;

c = 2/pi*[1, 0, -1/3, 0, 1/5, 0, -1/7]; % c is a vector representing the coefficients
max = numel(c); %determines the number of coefficients we have in the vector

for i=1:max
    f = cos(i*k*x); %creates a vector of cos(ikx)
    f_x = f_x + c(i)*f; %this makes the total f vector
end

%can also build using a matrix method in the for loop:
%fmat(i,:) = f; %creates a matrix storing all vectors
%then use:
%f_x= c0/2 + c(1)*fmat(1,:) + c(2)*fmat(2,:) + c(3)*fmat(3,:) + c(4)*fmat(4,:);

plot(x, f_x);