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 August 30th, 2016, 06:41 PM #1 Newbie   Joined: Jan 2014 Posts: 16 Thanks: 0 Finding the bounds of a ratio Sorry in advance if I've posted in the wrong section. given the set $\{r_i, r_{ii}, r_{iii}, ... , r_R\}$ where $r_i \geq r_{i+1}$ What are the bounds of this ratio if it has any? $$( \, log_2{\frac{(\sum_{i=1}^R{r_i})!}{\prod_{i=1}^R{(r _i!)}}}) \, :\sum_{i=1}^{R}{i \cdot r_i}$$ Last edited by iScience; August 30th, 2016 at 06:45 PM. August 30th, 2016, 07:35 PM   #2
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Quote:
 Originally Posted by iScience Sorry in advance if I've posted in the wrong section. given the set $\{r_i, r_{ii}, r_{iii}, ... , r_R\}$ where $r_i \geq r_{i+1}$ What are the bounds of this ratio if it has any? $$( \, log_2{\frac{(\sum_{i=1}^R{r_i})!}{\prod_{i=1}^R{(r _i!)}}}) \, :\sum_{i=1}^{R}{i \cdot r_i}$$
I can't solve it myself but I'm guessing you are taking the r_i to be positive integers?

-Dan August 30th, 2016, 08:08 PM #3 Newbie   Joined: Jan 2014 Posts: 16 Thanks: 0 oh oops. Yeah $$r \ \epsilon \ \mathbb{Z}_+$$ Last edited by iScience; August 30th, 2016 at 08:12 PM. September 1st, 2016, 11:43 PM #4 Newbie   Joined: Jan 2014 Posts: 16 Thanks: 0 Basically the domain for this ratio is a $set$ of positive integers, bounded from $[1 , inf)$ My goal is find the range of that ratio, given the domain. For all tested sets of values so far, I haven't found the range (value of the ratio) to ever reach 1. I can't even come up with a proof that this must be true for all cases. Therefore, continuing forward.. assuming that this is true (ratio < 1), I'd like to know what properties of a given set dictates the ratio's closeness to the value 1. Any help is truly appreciated. Tags analysis, bounds, discrete, discrete math, finding, ratio Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post wirewolf Algebra 1 May 24th, 2015 02:47 PM Proff Real Analysis 3 July 27th, 2013 01:40 AM Beevo Calculus 2 December 2nd, 2012 10:20 AM Tom92 Applied Math 1 May 16th, 2010 11:39 PM symmetry Algebra 1 May 10th, 2007 11:56 PM

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