I think I understand the concept of summations and Θ-notations, however, I don't really understand the question below.
If I have understood it correctly, I'm supposed to write out the summations (functions on the left), then compare their order of growths to the functions on the right (correct me if I'm wrong).
Now the part where I got stuck is: I'm not so sure as to what I should do with the summations.
There are actually more functions on the left but I deleted them to make the questioin look less messy.
It is somewhat weird that your summand does not involve any $i$'s, since you are summing from $i=1$ up to $n$. Assuming you did not make a mistake, \begin{align*} i(n) &= \sum_{i=1}^n (4 + \log n) = n(\log n + 4) \end{align*}
You have an $n\log n$ term and a $4n$ term. If you understand the $\Theta$-notation well, you should be able to answer this. For the other questions, you should expand the sum if there is one and see if you can rewrite it without the sum for the bound analysis.