
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
August 7th, 2017, 02:24 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, 03:48 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,243 Thanks: 1439 
Yes, common sense indicates that it's x, y and z that cycle.

August 7th, 2017, 03:51 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, 08:47 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 18,243 Thanks: 1439 
Yes.


Tags 
category, cyclic, put, question, sum 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Category theory question  ipp  Abstract Algebra  0  December 8th, 2013 09:39 AM 
elementary category theory question  pseudonym  Abstract Algebra  5  November 28th, 2008 12:59 PM 
question (group locally cyclic....)  sastra81  Abstract Algebra  1  February 27th, 2007 02:24 AM 
question (group locally cyclic  sastra81  Abstract Algebra  1  February 27th, 2007 02:18 AM 