Number Theory

    

Induction and Analogy in a Problem of Finite Sums

Authors: Ryan Zielinski

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.

Comments: 73 Pages. This work is licensed under the CC BY 4.0, a Creative Commons Attribution License.

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Submission history

[v1] 2016-07-07 12:02:36
[v2] 2016-07-25 10:05:25
[v3] 2021-06-08 16:33:39

Unique-IP document downloads: 376 times

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