Computing Algorithm Complexity - Confusion

Question

I have the following code snippet:

sum = 0;
for (i = 0; i < n; i++)
    for (j = 0; j < i; j++)
        sum++;

The complexity would be O(n^2), but if I want to dig a little more for the internal loop complexity then would it be (n (n-1))/2 or (n-1)!?

Answer 1

Yes, O(n^2), but actually 0+1+...+n-1=n(n-1)/2 = O(n^2), definitely not (n-1)!