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Trapezoidal Numbers

by Carlton Gamer (Colorado College), David W. Roeder (Colorado College), and John J. Watkins (Colorado College)

This article originally appeared in:
Mathematics Magazine
March, 1985

Subject classification(s): Numbers and Computation | Patterns and Sequences
Applicable Course(s): 3.7 Discrete Math | 4.1 Introduction to Proofs | 4.3 Number Theory

Which numbers can be written as a sum of consecutive positive integers, such as 12 = 3 + 4 + 5? The answer: all positive integers except the powers of 2. The authors prove this result and connect it to music.

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Capsule Course Topic(s):
Number Theory | Numbers With Special Forms or Properties
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