remember the days when Nicholas O. showed elegantly that 1+1/2+1/3+1/4+1/5+... is unbounded? he stated, according to http://en.wikipedia.org/wiki/Nicole_Oresme that 1+1/2+(1/3+1/4)+(1/5+1/6+1/7+1/8)+ ... must be greater than 1+1/2+(1/4+/4)+(1/8+1/8+1/8+1/8)+... and so must be greater than 1+1/2+1/2+1/2+... a nice tidbit given by eric's http://mathworld.wolfram.com/HarmonicSeries.html My surprise: good old Mathematica 4.0 gives no solace for each of those cool brackets: Limit[Sum[1./k,{k,2^n+1,2^(n+1)}], n->Infinity] aka limit of HarmonicNumber[2^(n+1)]-HarmonicNumber[2^n] aka limit of -PolyGamma[0, 1 + 2^n] + PolyGamma[0, 1 + 2^(1 + n)] but, numerically, it looks a lot like Log[2]. The question "why?" is sometimes translated as "proof?" Wouter.