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若√a-1+√ab-2=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2012)(b+2012)的值.
人气:201 ℃ 时间:2020-06-16 07:31:00
解答
√(a-1)+√(ab-2)=0
√(a-1)=√(ab-2)=0
a-1=0,a=1
ab-2=0,b=2
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2012)(b+2012)
=1/1×2+1/2×3+1/3×4+……+1/2013×2014
=1/1-1/2+1/2-1/3+1/3-1/4+……+1/2013-1/2014
=1-1/2014
=2013/2014
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