A Generalization of Euler's Limit. (15th March 2023)

• Record Type: Journal Article
• Authors: Chakraborty, Bikash; Chakraborty, Sagar
• Is Part Of: College mathematics journal. Volume 54:Number 2(2023)
• Page Start: 140
• Page End: 141
• Publication Date: 2023-03-15
• Subjects: 40A05 -- 11B83; Mathematics -- Study and teaching -- Periodicals; Mathematics -- Periodicals; Mathematics; Mathematics -- Study and teaching; Periodicals; 510.071
• DOI: 10.1080/07468342.2023.2183543
• Languages: English
• ISSNs: 0746-8342

Abstract

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 .