What does the symbol $\sum_{\mathrm{cyc}}$ mean? mean? For example some write : $"$The Inequality is then equivalent to $$\sum_{\mathrm{cyc}}a^2+2\sum_{\mathrm{cyc}}\sqrt{a}\ge9"$$
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It means you add up over the variables in play. For example, if the original expression had $a, b, c, d$, you'd add up over those, e.g., $\sum_{cyc} a^2 = a^2 + b^2 + c^2 + d^2$.
More interesting is when you have expressions such as $\sum_{cyc} ab$ which in the context of a problem with $a,b,c,d$ would generally mean
$$ \sum_{cyc} ab = ab + bc + cd + da$$
I'm not sure if this convention is set in stone, but it's a useful shorthand. Be sure to evaluate it in context.
Simon S
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1The variables in play with my inequality are $a,b,c$, so $$\sum_{\mathrm{cyc}}a^2+2\sum_{\mathrm{cyc}}\sqrt{a}\ge9\iff a^2+b^2+c^2+2\sqrt a+2\sqrt b+2\sqrt c\geq9$$ – user196552 Nov 30 '14 at 17:54
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Is it right Simon? – user196552 Nov 30 '14 at 18:02
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2Looks reasonable. Just double check it in the context of the problem to make sure it really does make sense. – Simon S Nov 30 '14 at 18:06
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ok thanks for your help – user196552 Nov 30 '14 at 18:24
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1but does the cyc stand for anything? – user71207 Apr 20 '21 at 09:21
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1@user71207 I know this is kinda late, and you probably already figured it out, but it stands for cyclic. Since you are adding up on the cyclic permutations of the variables – Bruno Andrades May 30 '22 at 05:25