诺|a-1|+|ab-2|=0,求1/ab+1/(a+1)(b+10)+1/(a+2)(b+2)+.+1/(a+2009)(b+2009)的值

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诺|a-1|+|ab-2|=0,求1/ab+1/(a+1)(b+10)+1/(a+2)(b+2)+.+1/(a+2009)(b+2009)的值
诺|a-1|+|ab-2|=0,求1/ab+1/(a+1)(b+10)+1/(a+2)(b+2)+.+1/(a+2009)(b+2009)的值

诺|a-1|+|ab-2|=0,求1/ab+1/(a+1)(b+10)+1/(a+2)(b+2)+.+1/(a+2009)(b+2009)的值
a=1.ab=2.所以:b=2.
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2009)(b+2009)
=1/1*2+1/(1+1)(2+1)+1/(1+2)(2+2)+.+1/(1+2009)(2+2009)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/2010-1/2011)
=1-1/2011
=2010/2011

a=1 ab=2 b=2 原式=1/2+1/6+1/10+……+1/4040101=2010/2011
规律:设整数为n
(a+n)*(b+n)=n的平方+3n+2
原式=(n+1)/(n+2)