Details

Autor(en) / Beteiligte

• Litvinov, Semyon
• Marko, František

Titel

Sums of Powers of Consecutive Integers and Pascal's Triangle

Ist Teil von

• The College mathematics journal, 2020-01, Vol.51 (1), p.25-31

Ort / Verlag

Washington: Taylor & Francis

Erscheinungsjahr

2020

Quelle

Taylor & Francis

Beschreibungen/Notizen

• We provide a new self-contained argument showing that, given a non-negative integer p, the coefficients of the closed forms of sums of kth powers of the first n natural numbers are unique, and can be recovered simultaneously for all k = 0, 1,…, p by finding the inverse of a matrix generated by a truncated Pascal’s triangle. An effective procedure for calculating the coefficients for a fixed k is given. We believe that the material presented in this article would be most suitable to students with a solid background in discrete mathematics. It can be used by instructors as a non-trivial application in a linear algebra or a real analysis course.