  We show that every real polynomial $f$ nonnegative on $[-1,1]^{n}$ can be
approximated in the $l_{1}$-norm of coefficients, by a sequence of polynomials
$\{f_{\ep r}\}$ 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 \textit{explicit} approximation sequence. Then
we show that if the Moment Problem holds for a basic closed semi-algebraic set
$K_S\subset\R^n$ with nonempty interior, then every polynomial nonnegative on
$K_S$ can be approximated in a similar fashion by elements from the
corresponding preordering. Finally, we show that the degree of the perturbation
in the approximating sequence depends on $\epsilon$ as well as the degree and
the size of coefficients of the nonnegative polynomial $f$, but not on the
specific values of its coefficients.
