观察下列等式1/(1*2)=1-1/2 1/(2*3)=1/2-1/3 1/(3*4)=1/3-1/4将以上三个灯市两边分别相加得:1/(1*2)+1/(2*3)+1/(3*4)=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/41.猜想并写出:1/[n(n+1)]=?2.直接写出下列各试的计算结果:(1)1/(1*2)+1/(2*3

观察下列等式1/(1*2)=1-1/2 1/(2*3)=1/2-1/3 1/(3*4)=1/3-1/4将以上三个灯市两边分别相加得:1/(1*2)+1/(2*3)+1/(3*4)=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/41.猜想并写出:1/[n(n+1)]=?2.直接写出下列各试的计算结果:(1)1/(1*2)+1/(2*3
观察下列等式
1/(1*2)=1-1/2 1/(2*3)=1/2-1/3 1/(3*4)=1/3-1/4
将以上三个灯市两边分别相加得:
1/(1*2)+1/(2*3)+1/(3*4)=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/4
1.猜想并写出:1/[n(n+1)]=?
2.直接写出下列各试的计算结果:
(1)1/(1*2)+1/(2*3)+1/(3*4)+...+1/(2006*2007)=?
(2)1/(1*2)+1/(2*3)+1/(3*4)+...+1/[n(n+1)]=?
要有解题思路 答案我已经有
1.n-1/(n+1)
2.(1)2006/2007 (2)n/(n+1)
没有一个全对的 太令我失望鸟....
书的答案是这样的

观察下列等式1/(1*2)=1-1/2 1/(2*3)=1/2-1/3 1/(3*4)=1/3-1/4将以上三个灯市两边分别相加得:1/(1*2)+1/(2*3)+1/(3*4)=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/41.猜想并写出:1/[n(n+1)]=?2.直接写出下列各试的计算结果:(1)1/(1*2)+1/(2*3
你的1题答案肯定错了!
因为：
1/[n(n+1)]=(n+1-n)/[n(n+1)]
=（n+1）/[n(n+1)]-n/[n(n+1)]
=1/n-1/（n+1）
这个当公式代入2题
(1)1/(1*2)+1/(2*3)+1/(3*4)+...+1/(2006*2007)
=1-1/2 +1/2-1/3 +1/3 -1/4 ...+1/2006-1/2007
=1-1/2007
=2006/2007
(2)同理
1/(1*2)+1/(2*3)+1/(3*4)+...+1/[n(n+1)]
=1-1/(n+1)
=n/(n+1)

1/[n(n+1)]=1/n-1/(n+1)
1/(1*2)+1/(2*3)+1/(3*4)+...+1/(2006*2007)
=(1/1-1/2)+(1/2-1/3)+……+(1/2006-1/2007)
=1-1/2007
=2006/2007
(2)1/(1*2)+1/(2*3)+1/(3*4)+...+1/[n(n+1)]
=(1/1-1/2)+(1/2-1/3)+……+[1/n-1/(n+1)]
=1-1/(n+1)
=n/(n+1)

1. 1/n-1/(n+1)
2. (1) =1-1/2+1/2-1/3+1/3-1/4+……+1/2006-1/2007=1-1/2007=2006/2007
(2) =1-1/2+1/2-1/3+1/3-1/4+……+1/n-1/(n+1)=1-1/(n+1)=n/(n+1)
自己错了还怪别人，脑袋被门夹了。。。

1.
1/[n(n+1)]=1/n-1/(n+1)
2.
(1) 1/(1*2)+1/(2*3)+1/(3*4)+...+1/(2006*2007)
=1-1/2 +1/2-1/3 +1/3 -1/4 ...+1/2006-1/2007
相邻2项一正一负，都消掉了
=1-1/2007
=2006/2007
(2)1/(1*2)+1/(2*3)+1/(3*4)+...+1/[n(n+1)]
=1-1/2 +1/2-1/3 +1/3 -1/4 ...+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)

要拆项
1/(1*2)=1-1/2
1/(2*3)=1/2-1/3
1/(3*4)=1/3-1/4
.....
1/(n*(n+1))=1/n-1/(n+1)
连续消去即可得到结果

1.:1/n-1/(n+1)
2(1):原试=1-1/2+1/2-1/3+1/3-1/4...+1/2006-1/2007
=1-1/2007
=2006/2007
(2)同理＝1－1／（n+1)
=n/(n+1)
我对了啊!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

有了你还问