## Asymptotic Summations

Prove the following :

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

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

where \(i\) is in radians.

Prove the following :

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

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

where \(i\) is in radians.