Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) ; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) ; Processo FAPESP: 09/13832-9 ; Processo FAPESP: 13/23606-1 ; Let N be a positive integer and x(j) be N equidistant points. We propose an algorithmic approach for approximate calculation of sums of the form Sigma(N)(j=1) F(x(j)). The method is based on the Gaussian type quadrature formula for sums, Sigma F-N(j =1)(x(j)) approximate to Sigma B-n(k=1)n,k F(g(n,k)(N)), n