$(5$ points$)$

Solve the following mathematical recurrence:

$T(n)=\{\begin{array}{cc}1,& n=1\\ 2T(\frac{n}{2})+n,& n>1\text{a}\text{n}\text{d}nis\text{a}\text{p}\text{o}\text{w}\text{e}\text{r}of& 2\end{array}$

${?}^1$ Note that nothing has been specified about this being a complete binary tree or if it is balanced in height, etc. So please don't make such assumptions. All that matters is that it is a binary tree.

$($Note: Your answer should provide a closed form expression for $T(n).)$