A Generalization of Euler's Limit. (15th March 2023) - Chakraborty, Bikash; Chakraborty, Sagar
Summary: The famous Euler's limit is lim n → ∞ ( n + 1 n ) n = e . In this note, we observe yet another generalization of Euler's limit as follows: Let { a n } and { b n } be two sequence of real numbers such that an > 1 and a n → 1 and bn is satisfying the asymptotic formula b n ∼ k a n − 1, where k  > 0, then lim n → ∞ a n b n = e k .