Linking summations with their correct function(s)

Question

Guys can you please guide me step by step on how to link given functions with the functions to choose from. So for example a function $g(n)\in \Theta n^2$ and if there is no match then you say there is no match. The problem is that I did some of the exercises by guessing, but I would like to know how to link these summations with their correct functions mathematically.

$f(n) = \Sigma^n_{i=1}\Sigma^i_{j=1} 1$

$i(n) = \Sigma^n_{i=1}[4 + log(n)]$

Choose from:

$log_2(n)$

$n$

$n log_2(n)$

$n (log_2(n))^2$

$n^2$

$n^2 log_2(n)$

$n^3$

$2^n$

$2^{2n}$

$n!$

$n^n$

no match

Answer 1

$$f(n) =\sum^n_{i=1}\sum^i_{j=1} 1=\sum^n_{i=1}i=\frac {n(n+1)}2 $$

$$i(n) = \sum^n_{i=1}[4 + \log(n)]= n(4 + \log n)$$