Let
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
be a natural number. Prove that
For any real number
![x](/media/m/f/1/8/f185adeed9bd346bc960bca0147d7aae.png)
, the number
![\lfloor x \rfloor](/media/m/c/c/2/cc22bc897f71e3436c8e79a0a632e862.png)
represents the largest integer smaller or equal with
![x](/media/m/f/1/8/f185adeed9bd346bc960bca0147d7aae.png)
.
%V0
Let $n$ be a natural number. Prove that $$\left\lfloor \frac{n+2^0}{2^1} \right\rfloor + \left\lfloor \frac{n+2^1}{2^2} \right\rfloor + \cdots + \left\lfloor \frac{n+2^{n-1}}{2^n} \right\rfloor = n\text{.}$$
For any real number $x$, the number $\lfloor x \rfloor$ represents the largest integer smaller or equal with $x$.