Abstract
A new asymptotic formula for the constant e is proposed by the continued fraction approximation. As a consequence, we deduce inequalities for the sequence \((1+1/n)^n\), and show an application of the inequalities to the proof of Keller’s limit. Numerical computations and comparisons are conducted to illustrate the superiority of our new inequalities.
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Acknowledgements
Computations made in this paper were performed using Maple software. The research of the Dawei Lu was supported by the National Natural Science Foundation of China (Grant Nos. 11371077 and 11571058). The research of the fourth author was supported by the National Natural Science Foundation of China (Grant No. 11471065).
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Fang, S., Lai, L., Lu, D. et al. On Some Convergence to the Constant \(\varvec{e}\) and Proof of Keller’s Limit. Results Math 73, 69 (2018). https://doi.org/10.1007/s00025-018-0831-8
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DOI: https://doi.org/10.1007/s00025-018-0831-8