% This uses the integration formula to calculate the remainder. This was not
% demonstrated in the class. quad function is used for Numerical
% Integration. You can put a loop on line 7 from say 1:999 and then break
% when the value in line 7 becomes less than 10^(-3).
n = 3 ;
x = 0.5 ;
fun = @(t)(((x-t).^n)*((t.^(n+1))*((-1).^n)/((n+1)*((1+t).^(n+1))))) ;
(1/factorial(n)) * quad (fun, 0, x)