function [y,err] = pi_approx2(n)
% y = pi_approx2(n) computes an approximation y of pi using the formula
% pi = 4-8*sum_k 1/(16*k^2-1)
% with the summation starting from the largest indices
%
% [y,err] = pi_approx2(n) in addition computes the error err = |y-pi|

% round the input down to the next integer (to make sure it is one)
n = floor(n);
x = 0;
for j = n:-1:1
    x = x+1/(16*j^2-1);
end
y = 4-8*x;

err = abs(y-pi);