13 A computer programmer needed to write a program that computes n! for all non-negative integer values of n. Rather than using a recursive routine, he used the fact that n! = T(n + 1), and used equation 6.16 to approximate T(n+1). He then rounded this approximation to the nearest integer, since the factorial will always be an integer. Since the two term approximation is clearly accurate enough for n = 1, and only gets more accurate as n→ ∞o, he figured this would work for all n. What was wrong with his logic? ~ 1+ (6.16) 12n 13) Although the relative error gets better as n gets large, the absolute error will increase to the point that the error will be more than 1. For example, this algorithm will produce 8!= 40318, when the true value is 40320.