function [y,err] = pi_approx(n)
% y = pi_approx(n) computes an approximation y of pi using the formula
% pi = 4-8*sum_k 1/(16*k^2-1)
%
% [y,err] = pi_approx(n) in addition computes the error err = |y-pi|

y = 4;
for j = 1:n
    y = y-8/(16*j^2-1);
end

err = abs(y-pi);