disp('-------------p1.6.6-------------')
n=[18:23]
Rn=(7.^(-n))/6 +(5.^(-n))/4
pause


disp('-------------p1.6.6----NUMERICAL----')
%% matlab can only store 16 significant digits
for n=15:25
    k = (1:n);
    x = rand(1000,1)/3; %[0:.01:1/3];
    z = (1-x)./(1+x);
    lnZ = log(z);
    x0 = 1/6;
    y1 = (x-x0)./(1-x0);
    y2 = (x-x0)./(1+x0);

    p = log(1-x0);
    q = log(1+x0);
    for t=k
        p = p - y1.^t/t;
        q = q + (-1)^(t+1)*y2.^t/t;
    end
    Tn = p - q;
    maxErr = max(abs(Tn- lnZ ));
    fprintf(1,'[n=%d] maxErr1 = %g\n', n, maxErr);
    if maxErr < 10^(-15)
        break;
    else
        pause(.5)
    end
end