A SUM OF AN ALTERNATING SERIES INVOLVING CENTRAL BINOMIAL NUMBERS AND ITS THREE PROOFS
A sum of an alternating series involving central binomial numbers and its three proofs
한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2022, v.29 no.1, pp.31-35
https://doi.org/https://doi.org/10.7468/jksmeb.2022.29.1.31
Li, Yue-Wu
(School of Mathematics and Statistics, Hulunbuir University)
Qi, Feng
(School of Mathematical Sciences, Tiangong University)
Li, Yue-Wu,
&
Qi, Feng.
(2022). A SUM OF AN ALTERNATING SERIES INVOLVING CENTRAL BINOMIAL NUMBERS AND ITS THREE PROOFS. 한국수학교육학회지시리즈B:순수및응용수학, 29(1), 31-35, https://doi.org/https://doi.org/10.7468/jksmeb.2022.29.1.31
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.
- keywords
-
Abel's theorem,
Abel's limit theorem,
sum,
alternating series,
central binomial number,
arcsine,
series expansion,
binomial expansion,
proof