The digital divide restricting the access of people living in developing areas to the benefits of modern information and communications technologies has become a major challenge and research focus. To well understand and finally bridge the digital divide, we first need to discover a proper measure to characterize and quantify the telecommunication service imbalance. In this regard, we propose a fine-grained and easy-to-compute imbalance index, aiming to quantitatively link the relation among telecommunication service imbalance, telecommunication infrastructure, and demographic distribution. The mathematically elegant and generic form of the imbalance index allows consistent analyses for heterogeneous scenarios and can be easily tailored to incorporate different telecommunication policies and application scenarios. Based on this index, we also propose an infrastructure resource deployment strategy by minimizing the average imbalance index of any geographical segment. Experimental results verify the effectiveness of the proposed imbalance index by showing a high degree of correlation to existing congeneric but coarse-grained measures and the superiority of the infrastructure resource deployment strategy.