x0 = 5 
x = x0;
N = 10;
% a = 2; b= 1;
a = 2.1; b= 1.1;

% for i = 1:N
%  x = x/a + b/x
% pause
% end

xx = zeros(1,N);
xx(1) = x0;
for i = 2:N
  xx(i) = xx(i-1)/a + b/xx(i-1);
  xx(i)
end

xstar = sqrt(a*b/(a-1));
m=5;
figure(1), semilogy(m:N, abs( xx(m:N)-xstar ), 'x')
figure(2), semilogx(m:N, abs( xx(m:N)-xstar ), 'x')
figure(3), loglog(m:N, abs( xx(m:N)-xstar ), 'x')
( xx(m:N)-xstar )./( xx(m-1:N-1)-xstar )