We show that every real polynomial f nonnegative on [−1, 1]n can be approximated in the l1-norm of coefficients, by a sequence of polynomials {fεr} that are sums of squares. This complements the existence of s.o.s. approximations in the denseness result of Berg, Christensen and Ressel, as we provide a very simple and explicit approximation sequence. Then we show that if the moment problem holds...