1/1*2+1/2*3+1/3*4+1/4*5......1/2007*2008

算这题前 你先算算这个

1/(1*2)=1/2

1/(1*2)+1/(2*3)=2/3

1/(1*2)+1/(2*3)+1/(3*4)=3/4

所以
1/1*2+1/2*3+1/3*4+1/4*5......1/2007*2008=2007/2008

这个是简便方法。。。要一般方法的看上面

=1/1-1/2+1/2-1/3+1/3-1/4+.....+1/2007-1/2008
=1-1/2008
=2007/2008

1/n(n+1)=1/n-1/(n+1)
原式=(1-1/2)+(1/2-1/3)+……+(1/1007-1/2008)
=1-1/2008=2007/2008

1/1*2+1/2*3+1/3*4+1/4*5......1/2007*2008
=1-(1/2)+(1/2)-(1/3)+...+(1/2007)-(1/2008)
=1-(1/2008)
=2007/2008

1/1*2+1/2*3+1/3*4+1/4*5......1/2007*2008
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2007-1/2008)
=1-1/2008
=2007/2008

原式＝（1－1/2）＋（1/2－1/3）＋。。。。。。（1/2007－1/2008）
＝1＋1/2－1/2＋1/3－1/3.。。。。。－1/2008
＝1－1/2008
＝2007/2008