The Non Orthogonal Multiple Access (NOMA) is a popular candidate for the next generation of wireless networks. Two advantages of NOMA are that it can achieve higher rate and support more users compared to the orthogonal multiple access (OMA). To support more users in NOMA system, we can assume there are infinite users in the system wanting to share one subchannel to derive the upper bound of the achievable rate of NOMA. In this article, the optimal power allocation function of infinite users in NOMA is derived which maximizes the average achievable rate of the system under the maximum power constraint. The performances of the proposed power allocation strategy are compared with simple case with only two users in NOMA. The simulation results show the gap between the average achievable rate and the outage probability of infinite users and two users in NOMA system.