Let n be a positive integer and let f(n)= 1²!+ 2²!+ 3²!+...+n²!

Determine polynomials P(n) and Q(n) such that f(n+2)= P(n)f(n+1)+ Q(n)f(n).

(In reply to re: Hint 2 by Joel)

I think (n^2 + 2n + 2)(n^2 + 2n + 3)..........(n^2 + 4n+4) is not a polynomial, because it can't be put into the form an^k+bn^(k-1)+cn^(k-2)+... w since you can't express all the terms in terms of n if it's unknown.

Posted by Gamer on 2007-01-24 17:26:58