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Apr 27, 2012 at 17:14 comment added user9072 It could really help if you provide some context. What type/quality of bound would you need? Or, is your last comment to be understood that the question is no longer relevant (say, since the application you had in mind does not work no matter the bound for this sum)?
Apr 27, 2012 at 15:48 comment added Rebekka Sadly, the integral isn't good enough... but I'm afraid my bound isn't working anyway... :-(
Apr 27, 2012 at 15:38 comment added Igor Rivin @charles: what do you mean by tails? These are all divergent...
Apr 27, 2012 at 12:45 comment added Gerry Myerson A good question, but not of research interest (unless you want bounds better than the best currently known). This website is for research; try math.stackexchange.com
Apr 27, 2012 at 11:25 comment added Charles Matthews The tails of such sums are easily bounded by integrals.
Apr 27, 2012 at 11:24 comment added Pietro Majer Isn't $\int^{n+1}_1 x^{-r}dx$ sufficient for your purposes?
Apr 27, 2012 at 11:08 history asked Rebekka CC BY-SA 3.0