formula n(n-1)/2

I know that n(n+1)/2 is getting the sum of 1 to n numbers.
How about the n(n-1)/2?

where and when do we use this formula? and what other formulas are related to these two?

I’d say, that if \frac{n(n+1)}{2} is som of n numbers, then \frac{(n-1)n}{2} is the sum of n-1 numbers, do you agree?

You know, it’s not easy to answer the question without the proper context…

Second formula can also be used to find out number of combinations how to choose two elements out of n, or how many elements Ai,j are in square matrix where i < j and probably one can find another dozen of descriptions…


As @betlista has said, n(n-1)/2 is the sum of the first (n-1) numbers, that is

1 + 2 + 3 + 4 + .......... + (n-1)

Now one might think that there is not much use for this formula, but when you do some research, you can find interesting uses for it. @betlista has explained a few uses. Here is a link which explains one usage