六年级一道要简算的计算题，急！！！！！！！！

来源：百度知道 编辑：UC知道 时间：2024/06/18 17:17:13
1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+……+1/19*20
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拜托啦！！！快点！急！
1/（1*2）+1/（2*3）+1/（3*4）+1/（4*5）+1/（5*6）+……+1/（19*20）
=

1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+……+1/19*20
= 1-1/2+1/2-1/3+....+1/19-1/20
= 1-1/20
= 19/20

1-1/2+1/2-1/3……+1/19-1/20
=1-1/20
=19/20

19/20
过程太复杂

1/n(n+2)=1/2[1/n-1/(n+2)]
1/1*3+1/2*4+1/3*5+1/4*6+...+1/18*20
=1/2(1-1/3+1/2-1/4+1/3-1/5+……+1/17-1/19+1/18-1/20)
=1/2(1+1/2-1/19-1/20)
=1/2(3/2-39/380)
=1/2*531/380
=531/760