A study of population dynamics in historic China defines b as the ratio of bandits to civilians

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A study of population dynamics in historic China defines b as the ratio of bandits to civilians (peasants and rulers) and s(b) as a measure of how successful the peasants are in fighting the bandits.
To prove results on how the population coped with various pressures and how easily erratic cycles may arise, the authors of the study needed to evaluate

Find the value of this limit.

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