Resolving dependencies of nested dependent summations

Question

If I have two or more nested summations in which the inner ones depend on the outer ones, how could I “remove” or resolve the dependencies?

In this case, for example:

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

What would be the easiest way to resolve the $j=i+1$ of the first inner summation?

Answer 1

Get rid of the inner summation and replace with the product (n-(i+1)).