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The spectral efficiency of single-cell multi-user large-scale distributed antenna system (DAS) is studied. Firstly, the closed-form expressions are derived for the uplink achievable rate with maximum ratio combining and the downlink achievable rate with maximum ratio transmission. Secondly, the limiting rates are also given when the ratio of the total number of base station (BS) antennas to the number of users goes to infinity. Thirdly, the results are validated via numerical simulations. It is shown that the closed-form expressions are very accurate with respect to the simulation results over a wide range of the ratio of the total number of BS antennas to the number of users, both the uplink and downlink achievable rates of the large-scale DAS are much larger than that of the co-located massive multiple-input multiple-output with the same antenna configuration and the theoretical results get more and more close to the limiting rates with increasing the ratio of the total number of BS antennas to the number of users.