AM/GM
Difficult
2016
Let real numbers $a_1$, $a_2$, $\cdots$, $a_{2016}$ satisfy $9a_i\ge 11a_{i+1}^2$ for $i=1, 2,\cdots, 2015$. Define $a_{2017}=a_1$, find the maximum value of $$P=\displaystyle\prod_{i=1}^{2016}(a_i-a_{i+1}^2)$$
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