Is the sum from i=1 to n for log(n/i) = Θ(n)?
Im studying for a test and appreciate your help. This is what I did: and got something else
$\sum_{i=1}^n \log(n/i)=\sum_{i=1}^n[\log n-\log i]=\left(\sum_{i=1}^n\log n\right)-\left(\sum_{i=1}^n \log i\right)=n\log n-\log n!=\log\left(\frac{n^n}{n!}\right) $