Time complexity of code running at most summation(N) times in a loop Let’s say I have a JavaScript loop iterating over input of size N. Let’s say all elements in N are unique, so the includes method traverses the entire output array on each loop iteration:

let out = []
for (x in N) }
  if (!out.includes(x)) {
    out.push(x)
  }
}


The worst case runtime of the code inside the loop seems to be not O(N), but the summation of N, which is substantially faster. 

Is this properly expressed as O(N^2) overall or is there a standard way to convey the faster asymptotic behavior given the fact that the output array is only of size N at the end of the loop?
If i understand you correctly, then the following holds:
$\sum_{k=1}^nk= \frac{n(n+1)}{2} \ge \frac{n^2}{2} = \Theta (n^2)$

Thus there is no asymptotic gain.