Find the square of sequence 1, negative 2, negative 4 N of (negative 1) minus the square of 1 power n What's the difference Find the square of sequence 1, negative 2, negative 4 N of (negative 1) minus the square of 1 power n And. Urgent

Find the square of sequence 1, negative 2, negative 4 N of (negative 1) minus the square of 1 power n What's the difference Find the square of sequence 1, negative 2, negative 4 N of (negative 1) minus the square of 1 power n And. Urgent

The sequence you want to sum is 1, - 2 & # 710; 2,3 & # 710; 2, - 4 & # 710; 2,5 & # 710; 2, - 6 & # 710; 2, ····, (- 1) & # 710; (n-1) × n & # 710; 2
When n is an even number, Sn = 1 & # 710; 2-2 & # 710; 2 + 3 & # 710; 2-4 & # 710; 2 + 5 & # 710; 2-6 & # 710; 2 + ··· + (n-1) & # 710; 2-N & # 710; 2
=﹣[(2ˆ2﹣1ˆ2)＋(4ˆ2﹣3ˆ2)＋(6ˆ2﹣5ˆ2)＋···＋((n-1)ˆ2﹣nˆ2)
=﹣[(2+1)＋(4+3)＋(6+5)＋···＋(2n-1)]
=﹣[3＋7＋11＋···＋(2n-1)]
=﹣n[3＋(2n-1)]/2
=﹣nˆ2/2
When n is odd, n-1 is even, Sn = s (n-1) + n = - (n-1) & # 710; 2 / 2 + n = - (n & # 710; 2 + 1) / 2