I'm studying discrete math for tomorrow's exam and got stuck in the below question. I tried to google it and couldn't find anything useful.
Prove the following sum is $\Theta (n^2)$ (we have to find $O(n^2)$ and $\Omega (n^2)$)
$P(n)= 1+2+3+4\cdots + n$
$P(n) = n+(n+1)+(n+2)+\cdots +2n$
Note you cannot use any formula you have to do it my algebraic manipulation. This might be simple but I am not getting any clue right now and I dont have solution of it.