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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.

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