Unmanned aerial vehicle (UAV)-enabled mobile edge computing has been recognized as a promising technology to flexibly and efficiently handle computation-intensive and latency-sensitive tasks in the era of fifth generation (5G) and beyond. In this paper, we study the problem of Service Provisioning for UAV-enabled mobile edge computiNg (SPUN). Specifically, under task latency requirements and various resource constraints, we jointly optimize the service placement, UAV movement trajectory, task scheduling, and computation resource allocation, to minimize the overall energy consumption of all terrestrial user equipments (UEs). Due to the non-convexity of the SPUN problem as well as complex coupling among mixed integer variables, it is a non-convex mixed integer nonlinear programming (MINLP) problem. To solve this challenging problem, we propose two alternating optimization-based suboptimal solutions with different time complexities. In the first solution with relatively high complexity in the worst case, the joint service placement and task scheduling subproblem, and UAV trajectory subproblem are iteratively solved by the Branch and Bound (BnB) method and successive convex approximation (SCA), respectively, while the optimal solution to the computation resource allocation subproblem is efficiently obtained in the closed form. To avoid the high complexity caused by BnB, in the second solution, we propose a novel approximation algorithm based on relaxation and randomized rounding techniques for the joint service placement and task scheduling subproblem, while the other two subproblems are solved in the same way as that of the first solution. Extensive simulations demonstrate that the proposed solutions achieve significantly lower energy consumption of UEs compared to three benchmarks.