English

Induction and Analogy in a Problem of Finite Sums

General Mathematics 2019-01-14 v2

Abstract

What is a general expression for the sum of the first n integers, each raised to the mth power, where m is a positive integer? Answering this question will be the aim of the paper....We will take the unorthodox approach of presenting the material from the point of view of someone who is trying to solve the problem himself. Keywords: analogy, Johann Faulhaber, finite sums, heuristics, inductive reasoning, number theory, George Polya, problem solving, teaching of mathematics

Keywords

Cite

@article{arxiv.1608.04006,
  title  = {Induction and Analogy in a Problem of Finite Sums},
  author = {Ryan Zielinski},
  journal= {arXiv preprint arXiv:1608.04006},
  year   = {2019}
}

Comments

73 pages. For the differences between versions, see the "Note to the Reader" of version 2