code class$=$"asciimath"$>$Let $,$f$\_($n$)($x$)=(1)/($n$)\backslash$sum$\_($k$=0)^$n $\backslash$sqrt$($k$($n$-$k$))(($n$!)/($k$!($n$-$k$)!))$x$^($k$)(1-$x$)^($n$-$k$)$ for xin$[0,1],$n$=1,2,3,$dots If $\backslash$lim$\_($n$->\backslash$infty $)$f$\_($n$)($x$)=$f$($x$)$ for xin$[0,1],$ then the maximum value of f$($x$)$ on $0,1$ is