Sum rules for electromagnetic transitions offer valuable insight into atomic nuclei. The Thomas-Reiche-Kuhn (TRK) sum rule on electric dipole transitions, for instance, directly reflects the exchange components of the nuclear force. In this work, the authors perform ab initio calculations of the multipole response of closed-shell nuclei from ⁴He to ⁷⁸Ni using various chiral two- and three-nucleon interactions and the in-medium-similarity-renormalization group (IMSRG) to incorporate key ground-state correlations. The TRK sum rule for ¹⁶O and ⁴⁰Ca agrees well with experiment, demonstrating an advance over competing many-body methods. This framework thus provides a benchmark for other ab initio calculations of integrated nuclear response properties.