function out=fN(x,N)
%
% computes the Nth partial sum of the fourier series for f(x)
%
out=zeros(size(x)); % initialize output
L=x(end);

a0=1;               % for a0
out=out + a0/2;
fprintf('\n Adding...(to %d)',N);   % print statement
for n=1:N
  fprintf('..%d',n);                % print statement
  k=2*n-1;
  an=0;
  bn=2/(k*pi);
  out = out + an*cos(k*pi*x/L) + bn*sin(k*pi*x/L);
end
fprintf('\n');                      % print statement