A Generalization of Euler’s Limit

SummaryThe famous Euler’s limit is limn→∞(n+1n)n=e. In this note, we observe yet another generalization of Euler’s limit as follows:Let {an} and {bn} be two sequence of real numbers such that an > 1 and an→1 and bn is satisfying the asymptotic formula bn∼kan−1, where k > 0, then limn→∞anbn=ek.