已知|ab-2|与(b-1)2次方互为相反数,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...1/(a+2006)(b+2006)的值

已知|ab-2|与(b-1)2次方互为相反数,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...1/(a+2006)(b+2006)的值
已知|ab-2|与(b-1)2次方互为相反数,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...1/(a+2006)(b+2006)的值

已知|ab-2|与(b-1)2次方互为相反数,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...1/(a+2006)(b+2006)的值
|ab-2|>=0
(b-1)^2>=0
|ab-2|与(b-1)^2互为相反数
则
|ab-2|=(b-1)^2=0
ab-2=0
b-1=0
a=2
b=1
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...1/(a+2006)(b+2006)
=1/2*1+1`/(2+1)(1+1)+1/(2+2)(1＋2)+.+1/(2+2006)(1+2006)
=1/1*2+1/2*3+1/3*4+.+1/2007*2008
=1-1/2+1/2-1/3+1/3-1/4+.+1/2007-1/2008
=1-1/2008
=2007/2008

因为二者大于等于0，又因为互为相反数，所以二者等于0。所以b＝1，所以a＝2。所以原式得1／2＋1／（3*2）＋1／（4*3）＋...＋1／（2007*20006）＝1／2＋1／2－1／3＋1／3－1／4....＋1／2005－1／2006＋1／2006－1／2007＝1－1／2007＝2006／2007