Using a symmetry-based argument, we prove the well-known formula for the sum of the first n integers

Orosi, Greg

OSU Libraries Digital Journal Publishing (Ohio State University)

Proof Without Words: Sum ofthe First n IntegersGreg Orosi, American University of SharjahAbstract: Using a symmetry-based argument, we prove the well-known formula for the sum of the first nintegers.Keywords: proof, geometry, integersn n(n+ 1) n(n+ 1) 2n(n+ 1) n(n+ 1) n(n+1)2Sn =n∑n=1i = 1 + 2 + · + n = n(n+ 1)2Greg Orosi, gorosi@ucalgary.ca, is currently an Associate Professorin the Department of Mathematics and Statistics at the American Uni-versity of Sharjah. His primary research areas include computationalfinance, empirical finance, and numerical methods applied to derivativepricing. However, in recent years, he also made some minor contribu-tions to mathematics education by providing proofs of some well-knownmathematical results.Ohio Journal of School Mathematics 80 Page 33

Proof Without Words: Sum of the First n Integers

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Proof Without Words: Sum of the First n Integers

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