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Note that "sum of the numbers from 1 to N" is not the same as "summing the numbers from 1 to N".

It's actually O(1). It's (N * (N+1))/2

that's what I said "constant time"

Your post is missing some required punctuation which would've made that easier to see.

what about (n(n+1)/2)< 1000 n^2 ? .

He interpreted it as "the time complexity of computing the sum of the numbers from 1 to n", which using the formula you just gave takes O(1) time.

The fastest algorithm for computing the sum 1 + 2 + 3 + .. + n is constant. But the result of the sum is O(n^2).

You can use that result to conclude that algorithms like for example bubble sort has a worst case running time of O(n^2), since it does (n-1) + (n-2) + ... + 1 swaps in the worst case during the whole sorting.