PROOF WITHOUT WORDS: RELATIONSHIP BETWEEN THE SUM OF NATURAL NUMBERS AND THE SUM OF THE PRODUCT OF TWO CONSECUTIVE INTEGERS
Keywords:
sum of natural numbers, sum of the product of two consecutive numbers, proof without words, visual thinking.DOI:
https://doi.org/10.17654/0973563122001Abstract
The visual clue for the relationship between the sum of natural numbers and the sum of the product of two consecutive integers is presented. This relationship indicates the reason why the sum of integers, $1+2+\cdots+n$, is represented by a factor of $(n+1) n$.
Received: October 11, 2021
Accepted: December 3, 2021
References
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Yukio Kobayashi, Visual thinking of mathematical concepts, Far East J. Math. Edu. 10(2) (2013), 157-174.
Sara Katz, Moshe Stupel and Ruth Segal, Proofs without words with geometric representations: a trigger to self-efficacy and mathematical argumentation, Far East J. Math. Edu. 16(1) (2016), 21-56.
Yukio Kobayashi, Geometrical meaning of arithmetic series and in terms of the elementary combinatorics, Internat. J. Math. Edu. Sci. Tech. 42 (2011), 657-664. [Corrigendum 42 (2011), 1123.]
Yukio Kobayashi, Proof without words: relationship between the sum of triangular numbers, sum of natural numbers, and sum of square numbers, Far East J. Math. Edu. 21 (2021), 83-91.
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