Bewijs dat $\left\lfloor\frac{n+2^{0}}{2^{1}}\right\rfloor+\left\lfloor\frac{n+2^{1}}{2^{2}}\right\rfloor+\cdots+\left\lfloor\frac{n+2^{n-1}}{2^{n}}\right\rfloor =n.$ ( $n \in \mathbb{N}$)