Resolving nested dependent summation $ \sum_{i=1}^{n-1} \sum_{j=i+1}^{n} j $

Question

I have the following summation:

$$ \sum_{i=1}^{n-1} \sum_{j=i+1}^{n} j $$

In which the inner sum depends on the outer one, in the index on the bottom.

Is there a way to change the indexes in order to remove the dependence?

What is the easiest way to get a closed form from it?

Answer 1

Why do want to get rid of dependence inner sum is easy to calculate

Hint:

$$\sum_{j=i+1}^{n} j=\sum_{j=1}^{n} j-\sum_{j=1}^{i} j=\frac{n(n+1)}{2}-\frac{i(i+1)}{2}$$

Can you solve it from here?