This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 1

1997 German National Olympiad, 2

For a positive integer $k$, let us denote by $u(k)$ the greatest odd divisor of $k$. Prove that, for each $n \in N$, $\frac{1}{2^n} \sum_{k = 1}^{2^n} \frac{u(k)}{k}> \frac{2}{3}$.