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August 7th, 2017, 01:24 PM  #1 
Member Joined: Oct 2016 From: New York Posts: 56 Thanks: 14 Math Focus: Analysis and Differential Geometry  cyclic sum question (wasn't sure what category to put in)
This is my first time encountering this type of a problem, so I am wondering if someone can help me understand what this means: Let $x, y$ and $z$ be positive real numbers and $k$ a nonnegative integer.... then it proceeds to give an inequality whose left side is the following cyclic sum. $\sum_{cyc}\frac{x^{2k+2}+y^{2k+2}}{z^{2k+1}}$ I just want to know if I'm getting this right. Is it implied that the $k$ is not cycling? Does the sum mean $\frac{x^{2k+2}+y^{2k+2}}{z^{2k+1}} + \frac{z^{2k+2}+x^{2k+2}}{y^{2k+1}}+ \frac{y^{2k+2}+z^{2k+2}}{x^{2k+1}}$? 
August 7th, 2017, 02:48 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 17,725 Thanks: 1359 
Yes, common sense indicates that it's x, y and z that cycle.

August 7th, 2017, 02:51 PM  #3 
Member Joined: Oct 2016 From: New York Posts: 56 Thanks: 14 Math Focus: Analysis and Differential Geometry 
That's what I thought, but am I right about what the cyclic sum means?

August 7th, 2017, 07:47 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 17,725 Thanks: 1359 
Yes.


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