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 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?

Iâ€™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, itâ€™s not easy to answer the question without the proper contextâ€¦

Second formula can also be used to find out number of combinations how to choose two elements out of n, or how many elements A_{i,j} are in square matrix where i < j and probably one can find another dozen of descriptionsâ€¦

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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

link

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