Question

五年级数学寒假作业1/(1*2)+1/(2*3)+1/(3*4).....+1/(1999*2000)=?

急用，说出方法技巧。加分

Answer 1

1/1*2=(2-1)/1*2=2/1*2-1/1*2=1-1/2
1/2*3=(3-2)/2*3=3/2*3-2/2*3=1/2-1/3
其他以此类推
所以1/(1*2)+1/(2*3)+1/(3*4).....+1/(1999*2000)
=1-1/2+1/2-1/3+……+1/1999-1/2000
中间正负抵消
=1-1/2000
=1999/2000

Answer 2

1/(1*2)=1/1-1/2
1/(2*3)=1/2-1/3
以此类推
所以原式=1/1-1/2+1/2-1/3+1/3-1/4……+1/1999-1/2000
=1-1/2000
=1999/2000

Answer 3

1/(1*2)+1/(2*3)+1/(3*4).....=1-1/2+1/2-1/3+1/3-1/4.....+1/1999-1/2000

=1-1/2000

=1999/2000

Answer 4

1/(5*6) = 1/5 - 1/6
其他类似