[math-fun] series convergence problem

I guess the answer to this is a known "folk theorem" but have not seen it explicitly stated before PUZZLE: Given a finite-dimensional vector V=(v0,v1,v2,...,vk) define the function F(n) via F(n) = n^v0 * ln(n)^v1 * lnln(n)^v2 * lnlnln(n)^v3 * ... Then: for which vectors V is it true that some N>1 exists such that the series sum(n>N) 1/F(n) converges? -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)