Binomial Coefficient as Sum of a Sum

Question

Few days ago, I found this equation:

$ \sum_{i=1}^n \sum_{j>i} \frac{1}{2} = {n \choose 2} \frac{1}{2} $

I didn't manage to prove it. Does anyone of you know how to prove it?

Answer 1

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