What is the proof of of (N–1) + (N–2) + (N–3) + … + 1= N*(N–1)/2 [closed]

Answer 1

Try to make pairs of numbers from the set. The first + the last; the second + the one before last. It means n-1 + 1; n-2 + 2. The result is always n. And since you are adding two numbers together, there are only (n-1)/2 pairs that can be made from (n-1) numbers.

So it is like (N-1)/2 * N.