Question

1/1986×1987+1/1987×1988+1/1988×1989+1/1989×1990=？ 用简便方法计算

Answer 1

公式：1/n(n+1)=1/n-1/(n+1)
所以
1/1986×1987+1/1987×1988+1/1988×1989+1/1989×1990=
1/1986-1/1987+1/1987-1/1988+1/1988-1/1989+1/1989-1/1990=1/1986-1/1990
=4/3952140

Answer 2

原式为1+1+1+1-1/1986-1/1987-1/1988-1/1989
到这里就是靠考算工了……

Answer 3

1/1986×（1986+1）+1/1987×（1987+1）+1/1988×(1988+1)+1/1989×（1989+1）=4+1/1986+1/1987+1/1988+1/1989

1楼的答案明显错误，因为答案至少大于4。

Answer 4

每项接近1. 之和大约 = 4

无简便方法可算.

Answer 5

1/1986×1987+1/1987×1988+1/1988×1989+1/1989×1990
=1/1986-1/1987+1/1987-1/1988+1/1988-1/1989+1/1989-1/1990
=1/1986-1/1990
=4/1986*1990
=1/988035