% Script logsum2.m
% A faster series for ln(2)

n = input('Enter number of terms ');

c = 1.0 / 9.0;
t = 2.0 / 3.0;
s = t;
fprintf('%5d %20.10e %20.10e\n',1,t,s);
for k = 1 : n-1
   t = c * ((2*k-1)/(2*k+1))*t;
   s = s + t;
   fprintf('%5d %20.10e %20.10e\n',k,t,s);
end
fprintf('Exact value is %.10e\n',log(2))