About 35 years ago, either Murray Klamkin or Andrew Gleason mentioned this problem to myself and some other students, and said that you look at the first entry v_i that's unequal to 1. If it's greater than 1, the proposition is true; if it's less than or equal to 1 (or if all the entries equal 1), then it's false. I got the impression that this might have been a Monthly problem. Jim Propp On Tuesday, July 23, 2013, Warren D Smith <warren.wds@gmail.com> wrote:
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)
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