> \begin{align*} &A = \sum_{k\geq1}^{n}k\cdot \binom{n}{k} \\ \end{align*}
$A $ is the no of ways to form a committee of $k \geq 1$ people out of $n$ available individuals and select one head for the selected committee.
Empty committee is not possible. Therefore we select the head first in $n$ ways and then any subset out of $(n-1)$ remaining people in $2^{n-1} $ ways.
> \begin{align*} &A =n\cdot2^{n-1} \\ \end{align*}