Question

20+19.9-19.8-19.7+19.6+19.5-19.4-19.3+...+0.8+0.7-0.6-0.5+0.4+0.3-0.2-0.1等于多少？

Answer 1

法1：S = 20+19.9-19.8-19.7+19.6+19.5-19.4-19.3+...+0.8+0.7-0.6-0.5+0.4+0.3-0.2-0.1
= (20+19.9)-(19.8+19.7)+(19.6+19.5)-(19.4+19.3)+...+(0.8+0.7)-(0.6+0.5)+(0.4+0.3)-(0.2+0.1)
= [39.9 + 39.1 + 38.3 + ... + 1.5 + 0.7] - [39.5 + 38.7 + ...+ 1.1 + 0.3]
每个方括号内是 50 项等差数列， d = 0.8
S = (1/2)50(39.9+0.7) - (1/2)50(39.5+0.3) = 25(40.6-39.8) = 20
法2：更简单方法
S = 20+19.9-19.8-19.7+19.6+19.5-19.4-19.3+...+0.8+0.7-0.6-0.5+0.4+0.3-0.2-0.1
= 20+(19.9-19.8)-(19.7-19.6)+(19.5-19.4)-(19.3-19.2)+...+(0.7-0.6)-(0.5-0.4)+(0.3-0.2)-0.1
= 20

Answer 2

20+19.9-19.8-19.7+19.6+19.5-19.4-19.3+...+0.8+0.7-0.6-0.5+0.4+0.3-0.2-0.1
=20+(19.9-19.8)-(19.7-19.6)+(19.5-19.4)-(19.3-19.2)+...+(0.9-0.8)+(0.7-0.6)-(0.5-0.4)+(0.3-0.2)-0.1
=20+(0.1-0.1)+(0.1-0.1)+.....+(0.1.-0.1)
=20

Answer 3

因为它们的公差都是零点一…
这样其实中间是19.7。
可以变成19.7×5=98.5。