|ab-2|+|a-1|=0试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2003)(b+2003)的值

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|ab-2|+|a-1|=0试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2003)(b+2003)的值|ab-2|+|a-1|=0试求1/ab+1/(a+1)(

|ab-2|+|a-1|=0试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2003)(b+2003)的值
|ab-2|+|a-1|=0试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2003)(b+2003)的值

|ab-2|+|a-1|=0试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2003)(b+2003)的值
绝对值和大于等于0,相加等于0,若有一个大于0,则另一个小于0,不成立.
所以两个都等于0
所以ab-2=0,a-1=0
ab=2,a=1
b=2/a=2
原式=1/1*2+1/2*3+……+1/2004*2005
=1-1/2+1/2-1/3+……+1/2004-1/2005
=1-1/2005
=2004/2005

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