|ab-2|+|b-1|=0 求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.1/(a+2010)(b+2010)的值

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|ab-2|+|b-1|=0 求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.1/(a+2010)(b+2010)的值

|ab-2|+|b-1|=0 求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.1/(a+2010)(b+2010)的值
|ab-2|+|b-1|=0 求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.1/(a+2010)(b+2010)的值

|ab-2|+|b-1|=0 求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.1/(a+2010)(b+2010)的值
根据绝对值为非负数得
ab-2=0 b-1=0
b=1 a=2
于是
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.1/(a+2010)(b+2010)
=1/1x2+1/2x3+1/3x4+.+1/2011x2012
=1-1/2+1/2-1/3+1/3-1/4+.+1/2011-1/2012
=1-1/2012
=2011/2012

|ab-2|+|b-1|=0
ab-2=0
b-1=0
∴a=2
b=1
∴1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+......1/(a+2010)(b+2010)
=1/(1×2)+1/(2×3)+1/(3×4)+……+1/(2011×2012)
=1-1/2+1/2-1/3+1/3-1/4+……+1/2011-1/2012
=1-1/2012
=2011/2012