15 Oct
2008
15 Oct
'08
9:16 p.m.
Somehow I was recently reminded of this old and very cute math problem, which some of you may enjoy tackling: ----------------------------------------- Let x_n be a dense sequence in [0,1]. x_1 divides [0,1] into a left piece of length a_1 and a right piece b_1. Inductively, x_(n+1) divides one of the subintervals that {x_1,...,x_n} divide [0,1] into a left piece of length a_n and a right piece of length b_n. Prove that Sum_1^oo (a_n * b_n * (a_n + b_n)) = 1/3. ----------------------------------------- --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele