What's the proof for this summation with dependent variables?

Question

Given $0\leqslant i<j\leqslant n$

$\sum_{i=0}^n\sum_{j=0}^n i = \sum_{i=0}^n(n+1)*i$

It seems to work like a nested loop and gave the right answer when substituting n for any number but I don't know how to derive it.

Answer 1

$ \sum\limits_{j=0}^{n}i=i(n+1)$ because there are $n+1$ terms in the sum each having one fixed value $i$. Now sum over $i$ to finish.