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若ab-2的绝对值+(b-2)的平方=0.求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a

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若ab-2的绝对值+(b-2)的平方=0.求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2009)(b+2009)
若ab-2的绝对值+(b-2)的平方=0.求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a
易得b=2;a=1
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2009)(b+2009)
=1/2+1/(2×3)+1/(3×4)+……+1/(2010×2011)
=1/2+1/2-1/3+1/3-1/4+······1/2010-1/2011
=1-1/2011
=2010/2011