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Asymptotic Summations

Prove the following :

  1. \(\sum_{i=1}^{n} \frac{\log i}{i} = \Theta ((\log n)^2)\)

  2. \( \sum_{i=0}^{n} |\sin(i)| = \Theta(n)\)

    where \(i\) is in radians.

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