This paper presents new results concerning the effective practical computation of the membership function of the infinite sum (defined via the sup-Hamacher-norm convolution) of triangular fuzzy numbers. Namely, we shall calculate the limit distribution of the H-gamma-sum a approximately 1 + a approximately 2 + ... of triangular fuzzy numbers a approximately i, i is-an-element-of N, for gamma = 0, 1, 2.