The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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A SUM OF AN ALTERNATING SERIES INVOLVING CENTRAL BINOMIAL NUMBERS AND ITS THREE PROOFS

  • Li, Yue-Wu (School of Mathematics and Statistics, Hulunbuir University) ;
  • Qi, Feng (School of Mathematical Sciences, Tiangong University)
  • Received : 2021.07.06
  • Accepted : 2021.08.23
  • Published : 2022.02.28
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Abstract

In the note, by virtue of Abel's theorem and Abel's limit theorem in the theory of power series, the author provides three proofs for a sum of an alternating series involving central binomial numbers.

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Acknowledgement

The authors thank anonymous referees for their careful corrections to, valuable comments on, and helpful suggestions to the original version of this paper. The first author, Dr. Yue-Wu Li, was partially supported by the Doctors Foundation of Hulunbuir University (Grant No. 2018BS12) in China.

References

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  3. F.W.J. Olver, D.W. Lozier, R.F. Boisvert & C.W. Clark (eds.): NIST Handbook of Mathematical Functions. Cambridge University Press, New York, 2010; available online at http://dlmf.nist.gov/.
  4. F. Qi, C.-P. Chen & D. Lim: Several identities containing central binomial coefficients and derived from series expansions of powers of the arcsine function. Results Nonlinear Anal. 4 (2021), no. 1, 57-64; available online at https://doi.org/10.53006/rna.867047.