已知|a-1|+|ab-2|=0,求下列式子值:1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2014)(b+2014)=?

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已知|a-1|+|ab-2|=0,求下列式子值:1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2014)(b+2014)=?
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已知|a-1|+|ab-2|=0,求下列式子值:1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2014)(b+2014)=?
已知|a-1|+|ab-2|=0,求下列式子值:
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2014)(b+2014)=?

已知|a-1|+|ab-2|=0,求下列式子值:1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2014)(b+2014)=?
|a-1|+|ab-2|=0,那么要求a-1=0,ab-2=0,所以a=1,b=2
所以原式=1/(1×2)+1/(2×3)+1/(3×4)+……+1/(2015×2016)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/2015-1/2016)
=1-1/2+1/2-1/3+1/3-1/4+……+1/2015-1/2016
=1-1/2016
=2015/2016
望采纳