clear
clf

np = 100;
pp = zeros(np, 1);
for i = 1:np
    pp(i) = leibnizpi(i*100);
end

loglog((1:np)*100, pp - pi, 'o-')
hold on
loglog((1:np)*100, 0.01 ./ (1:np), '--')
grid on
legend('experiment', 'guess')

function piapprox = leibnizpi(n)
% leibnizpi calculate approximation to pi by summing n terms of Leibniz series
    piapprox = 0;
    s = 1;
    for i = 0:n
        piapprox = piapprox + s/(2*i + 1.0);
        s = -s;
    end
    piapprox = 4*piapprox;
end