已知|ab-2|+(a-1)²=0,求下面等式答案 - 知识问答

已知|ab-2|+(a-1)²=0,求下面等式答案

2个回答

根据题意得
ab-2=0 a-1=0
解得
a=1 b=2
于是
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2007)(b+2007)
=1/1x2+1/2x3+1/3x4+...+1/2008x2009
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2008-1/2009)
=1-1/2+1/2-1/3+1/3-1/4+...+1/2008-1/2009
=1-1/2009
=2008/2009

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