TWO COMBINATORIAL THEOREMS

Although the primary purpose of this article is to exhibit and prove two interesting relationships involving the binomial coefficients that we have not encountered elsewhere, 1 we have several subsidiary objectives. We endeavor to show how the relationships arose naturally in the course of solving o...

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Bibliographic Details
Published in:The Mathematics teacher 1967-05, Vol.60 (5), p.464-469
Main Authors: GLICKSMAN, A. M., RUDERMAN, H. D.
Format: Article
Language:English
Subjects:
Binomial coefficients
Indices of summation
Integers
Mathematical induction
Mathematical theorems
Mathematics teachers
Minimum value
Pascals triangle
Polynomials
Sine function
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Summary:Although the primary purpose of this article is to exhibit and prove two interesting relationships involving the binomial coefficients that we have not encountered elsewhere, 1 we have several subsidiary objectives. We endeavor to show how the relationships arose naturally in the course of solving other problems; we attempt to strip them of the usual aura of mystery that often surrounds a nontrivial mathematical result; and we encounter an aspect of mathematical induction not often mentioned to students, nor even known to many teachers of mathematics. In this way we hope to endow the article with heuristic as well as mathematical content.
ISSN:0025-5769
2330-0582
DOI:10.5951/MT.60.5.0464