|ab-2|-(b-1)(b-1)=0时,求1/ab+1/(a+1)(b+1)+ 1/(a+2)(b+2)+……+1/(a+1998)(b+1998)

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|ab-2|-(b-1)(b-1)=0时,求1/ab+1/(a+1)(b+1)+ 1/(a+2)(b+2)+……+1/(a+1998)(b+1998)

|ab-2|-(b-1)(b-1)=0时,求1/ab+1/(a+1)(b+1)+ 1/(a+2)(b+2)+……+1/(a+1998)(b+1998)
|ab-2|-(b-1)(b-1)=0时,求1/ab+1/(a+1)(b+1)+ 1/(a+2)(b+2)+……+1/(a+1998)(b+1998)

|ab-2|-(b-1)(b-1)=0时,求1/ab+1/(a+1)(b+1)+ 1/(a+2)(b+2)+……+1/(a+1998)(b+1998)
题目是不是:
|ab-2|+(b-1)²=0时,求1/ab+1/(a+1)(b+1)+ 1/(a+2)(b+2)+……+1/(a+1998)(b+1998).
由于|ab-2|、(b-1)²都是非负数,所以必有:
|ab-2|=0
(b-1)²=0
解之,得:
b=1
a=2
代入欲求式,得:
1/(1×2)+1/(2×3)+1/(3×4)+……+1/(1999×2000)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/1999-1/2000)
=1-1/2000
=1999/2000