Whether this function is concave?

Question

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. $x$?