The function $f(x)=\sum\limits_{n=0}^{N} \binom{N}{n}x^n(1-x)^{N-n}a_n$, where $0\le x\le1$, and $\{a_n\}$ is a increasing positive series w.r.t. $n$.
Then,whether the $f(x)$ is concave w.r.t. $x$?
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I would say $\sum_{n=0}^{N} \binom{N}{n}x^n(1-x)^{N-n}=1 \ \ $ for all x – georg Oct 17 '16 at 11:35
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Where is $a_n$? – Dave Oct 17 '16 at 11:36
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Apparently I don't understand. So my comment do not take into account. – georg Oct 17 '16 at 11:44