Theoretical Mathematics and Pedagogical Mathematics (한국수학교육학회지시리즈B:이론수학과 교직수학)

Korean Society of Mathematical Education (한국수학교육학회)
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A STUDY ON THE CONSISTENT INDUCTIVE JUSTIFICATION AND EXTENSION OF $\sum\limits_{k=1}^{n}k^{\alpha}$

$\sum\limits_{k=1}^{n}k^{\alpha}$의 일관된 귀납적 정당화 방법의 탐색과 그 확장에 대한 연구

  • Hyun Ju Jo (Sejong Yangji High School) ;
  • Bo Euk Suh (Department of Mathematics Education, Chungnam National University)
  • Received : 2025.04.12
  • Accepted : 2025.05.19
  • Published : 2025.05.31
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Abstract

This paper investigates a part of the Faulhaber formula studied in the hAlgebrai curriculum. Specifically, it examines the formula for $\sum\limits_{k=1}^{n}k^{\alpha}$ (α = 1, 2, 3). Based on textbook analysis, this study attempts to derive a general method of inductive justification for the formula when α = 1, 2, 3), and further extends it to the cases where α = 4, 5. First, through an analysis of previous research, two consistent methods of inductive justification were identified. One is the 'geometric rotational symmetry' method, and the other uses ratios. Second, using these two methods, the formula for $\sum\limits_{k=1}^{n}k^{\alpha}$ was inductively derived for α = 4, 5.

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References

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