How to make the sequence positive and negative Alternating like this? (expressed with the power of - 1) The answer is n (n-1) / 2 of (- 1), n = 0,1,2 Why?

How to make the sequence positive and negative Alternating like this? (expressed with the power of - 1) The answer is n (n-1) / 2 of (- 1), n = 0,1,2 Why?

If n is odd, n = 2K + 1, then (2k + 1) k is obtained. The parity of K determines the parity of the original formula when n is odd, that is, when n is odd, its parity also fluctuates. When n is even, it is similar, and the first two numbers are zero after being substituted