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August 7th, 2017, 02:24 PM   #1
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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 $\frac{x^{2k+2}+y^{2k+2}}{z^{2k+1}} + \frac{z^{2k+2}+x^{2k+2}}{y^{2k+1}}+ \frac{y^{2k+2}+z^{2k+2}}{x^{2k+1}}$?
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August 7th, 2017, 03:48 PM   #2
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Yes, common sense indicates that it's x, y and z that cycle.
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August 7th, 2017, 03:51 PM   #3
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That's what I thought, but am I right about what the cyclic sum means?
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August 7th, 2017, 08:47 PM   #4
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Yes.
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