Archive for binomial identity

an a-statistical proof of a binomial identity

Posted in Books, Statistics, University life with tags , , , , on May 15, 2014 by xi'an

When waiting for Andrew this morning, I was browsing through the arXived papers of the day and came across this “Simple Statistical Proof of a Binomial Identity” by P. Vellaisamy. The said identity is that, for all s>0,

\sum_{k=0}^n (-1)^k {n \choose k}\dfrac{s}{s+k} = \prod_{k=1}^n \dfrac{k}{k+s}

Nothing wrong with the maths in this paper (except for a minor typo using Exp(1) instead of Exp(s), p.2).  But I am perplexed by the label “statistical” used by the author, as this proof is an entirely analytic argument, based on two different integrations of the same integral. Nothing connected with data or any statistical  technique: this is sheer combinatorics, of the kind one could find in William Feller‘s volume I.