## Is $\sum_{i=1}^n i \in \Theta(n^2)$?

Please help me understand on how to prove or disprove the following. I have been practicing and doing others which are ok, but with this sum, it is rather confusing.

$$\sum_{i=1}^n i \in \Theta(n^2).$$

## Find the tight upper bound of $\sum_{i=1}^n \frac{i}{i+x_i}$, where the $x_i$’s are distinct in $\{1,2,…,n\}$

What is the tight upper bound of $$\sum_{i=1}^n \frac{i}{i+x_i}$$, where the $$x_i$$‘s are distinct integers in $$\{1,2,…,n\}$$?