1/1*3+1/2*4+1/3*5+.1/18*20=?
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/19 08:12:35
![1/1*3+1/2*4+1/3*5+.1/18*20=?](/uploads/image/z/5600308-4-8.jpg?t=1%2F1%2A3%2B1%2F2%2A4%2B1%2F3%2A5%2B.1%2F18%2A20%3D%3F)
1/1*3+1/2*4+1/3*5+.1/18*20=?
1/1*3+1/2*4+1/3*5+.1/18*20=?
1/1*3+1/2*4+1/3*5+.1/18*20=?
1/1×3 + 1/2×4 + 1/3×5 +...+ 1/18×20
= (1/2)×(1 - 1/3) + (1/2)×(1/2 - 1/4) +...+ (1/2)×(1/18 - 1/20)
= (1/2)×(1 - 1/3 + 1/2 - 1/4 + ...+ 1/17 - 1/19 + 1/18 - 1/20)
= (1/2)×(1 + 1/2 - 1/19 - 1/20)
= (1/2)×531/380
= 531/760