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This letter presents our study of throughput enhancement achieved by multiuser diversity (MUDiv) in a multiuser system using a new asymptotic approach. The MUDiv gain is evaluated by deriving a new asymptotic formula with a closed form, which is flexible to the number of MUDiv orders. To do this, we simplify a Puiseux series instead of a extreme value theory used in the previous researches. The formula shows that the MUDiv gain is independent of the signal-to-noise ratio, and it is applied to analyze proportional fair scheduling. Finally, this analysis is verified using Monte-Carlo simulations of scheduling algorithms.