Recently, 3D Gaussian Splatting (3DGS) has emerged as a significant advancement in 3D scene reconstruction, attracting considerable attention due to its ability to recover high-fidelity details while maintaining low complexity. Despite the promising results achieved by 3DGS, its rendering performance is constrained by its dependence on costly non-commutative alpha-blending operations. These operations mandate complex view dependent sorting operations that introduce computational overhead, especially on the resource-constrained platforms such as mobile phones. In this paper, we propose Weighted Sum Rendering, which approximates alpha blending with weighted sums, thereby removing the need for sorting. This simplifies implementation, delivers superior performance, and eliminates the ``popping'' artifacts caused by sorting. Experimental results show that optimizing a generalized Gaussian splatting formulation to the new differentiable rendering yields competitive image quality. The method was implemented and tested in a mobile device GPU, achieving on average $1.23\times$ faster rendering.