English

A Short Proof of Knuth's Old Sum

General Mathematics 2025-06-10 v2

Abstract

We give a short proof of the well-known Knuth's old sum and provide some generalizations. Our approach utilizes the binomial theorem and integration formulas derived using the Beta function. Several new polynomial identities and combinatorial identities are derived.

Keywords

Cite

@article{arxiv.2412.00040,
  title  = {A Short Proof of Knuth's Old Sum},
  author = {Kunle Adegoke},
  journal= {arXiv preprint arXiv:2412.00040},
  year   = {2025}
}

Comments

23 pages, no figures or tables