We consider the Cesàro sequence space ces p as a closed subspace of the infinite p -sum of finite dimensional spaces. We easily obtain many known results, for example, ces p has property (β) of Rolewicz, uniform Opial property, and weak uniform normal structure.We also consider some generalized Cesàro sequence spaces. Finally, we compute the von Neumann-Jordan and James constants of the two-dimensional Cesàro sequence space ces(2) p when 1 < p 2.