Asymptotic and 3-SAT problem in Algorithm Course my TA says just one of the following is True, anyone could describe me some detail about following three lines? 
1- if $f_i$ be a function of natural numbers to natural numbers and $f_i(n)=O(n)$ then $\Sigma_{i=1}^{n} f_i(n)=O(n^2)  $ 
2- for each positive asymptotic function we have : $ f(n)+ o (f(n))= \theta (f(n)) $
3- if $ L \in NP $  and $ L \leq_p 3-SAT$ (i.e: reduce L to 3-SAT in poly time) then L is NP-Complete. 

1 - Let be $f_i(n)=in \implies \ \forall i \in \mathbb{N} f_i(n)=O(n)$ and therefore $\sum_{i \in \mathbb{N}}^nf_i(n)=n\sum_{i \in \mathbb{N}}^ni=\Theta(n^3) \implies \sum_{i \in \mathbb{N}}^nf_i(n)\neq O(n^2)$ so this statement is false
3 - $\forall P\in {NP}\ P\leq_p 3-SAT$ thus if your statement is true $\forall L\in P\subseteq NP \ L\in NP-complete$ because $3-SAT$ is $NP-complete$ so this statemente is also false
