Question

|2−a|+(b+1)(b+1)=0,求(a+b)(a•a-ab+b•b)

若｜ab-2｜+｜b-1｜=0,试求1/ab+1/(a+b)(b+1)+…+1/(a+2003)(b+2003)
写出方法和最后的值

Answer 1

｜ab-2｜+｜b-1｜=0
绝对值相加为0则都等于0
所以ab-2=0，b-1=0
b=1,ab=2,所以a=2
所以
1/ab+1/(a+1)(b+1)+…+1/(a+2003)(b+2003)
=1/1*2+1/2*3+……+1/2004*2005
=1-1/2+1/2-1/3+……+1/2004-1/2005
=1-1/2005
=2004/2005