How to find out if hmslo is the sum of some n first numbers of the natural series?

Question

Mathematics

There is a number, you need to somehow check whether it is the sum of some n first numbers of the natural series?
I tried to convert , I ended up with the reverse , which I later found. But here's the problem, I won't be able to find out, n, because (n + 1) * n

Answer 1

So this is the same ... you solve a quadratic equation (opening the brackets you get n ^ 2 + n-2S = 0)
If the solution turned out to be a natural number, then S is the sum of the first n natural numbers.