Question

(+1)+(-2)+(+3)+(-4)+...+(+99)+(-100)这道题怎么做，急急急啊啊

Answer 1

(+1) + (-2) = (1-2) = -1

(+1) + (-2) + (+3) + (-4) = (1-2) + (3-4) = -1 -1 = -2
= (-1) X 4 / 2

(+1) + (-2) + (+3) + (-4) + (+5) + (-6) = (1-2) + (3-4) + (5-6) = -1 -1 -1 = -3
= (-1) X 6 / 2

绝对值最大是 -2，结果 -1 就是 (-1) X 2/2
绝对值最大是 -4，结果 -2 就是 (-1) X 4/2
绝对值最大是 -6，结果 -3 就是 (-1) X 6/2
那么
(+1) + (-2) + (+3) + (-4) + …… + (+99) + (-100)
= (-1) + (-1) + …… + (-1)
= -50
绝对值最大是 -100，结果就是 (-1) X 100/2 = -50

另一个方法，就把奇数、偶数分开来计算吧
1+3 =4 = 2X2 = [(3+1)/2]"
1+3+5 = 9 = 3X3 = [(5+1)/2]"
1+3+5+7 = 16 = 4X4 = [(7+1)/2]"
1+3+5+7+……+99 = [(99+1)/2]" = (100/2)" = 50X50 = 2500

(-2)+(-4) = -6 = -2X3 = -(4/2)(4/2+1)
(-2)+(-4)+(-6) = -12 = -3X4 = -(6/2)(6/2+1)
(-2)+(-4)+(-6)+(-8) = -20 = -4X5 = -(8/2)(8/2+1)
(-2)+(-4)+(-6)+(-8)++(-100) = -(100/2)(100/2+1) = -50X51 = -2550

最后把奇数的和与偶数的和再加起来
(+1) + (-2) + (+3) + (-4) + …… + (+99) + (-100)
= (+2500) + (-2550)
= -50

Answer 2

(+1)+(-2)+(+3)+(-4)+...+(+99)+(-100)=（-1）+（-1）+（-1）+（-1）+（-1）+（-1）+。。
一共 50个，所以=-50

Answer 3

1+1+1+...+1+(-100)
一共50个1
所以等于-50

Answer 4

原式=(1+3+7+.....+99)-（2+4+6+......+100）
=2500-2550
=-50
中间利用高斯的首尾相加的方法，一共有25组100，同理，后边括号里是25组102，得出结果

Answer 5

原式=（—1）x50
=—50

Answer 6

原式=-1+（-1)+……+（-1）=-1*（100/2）=-1*50=-50