数学有理数习题如果有理数a,b满足|ab-2|+(1—b)(1—b)=0,试求1/ab+ 1/(a+1)(b+1) + 1/(a+2)(b+2)+.+1/(a+2007)(b+2007)的值

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数学有理数习题如果有理数a,b满足|ab-2|+(1—b)(1—b)=0,试求1/ab+ 1/(a+1)(b+1) + 1/(a+2)(b+2)+.+1/(a+2007)(b+2007)的值
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数学有理数习题如果有理数a,b满足|ab-2|+(1—b)(1—b)=0,试求1/ab+ 1/(a+1)(b+1) + 1/(a+2)(b+2)+.+1/(a+2007)(b+2007)的值
数学有理数习题
如果有理数a,b满足|ab-2|+(1—b)(1—b)=0,试求1/ab+ 1/(a+1)(b+1) + 1/(a+2)(b+2)+.+1/(a+2007)(b+2007)的值

数学有理数习题如果有理数a,b满足|ab-2|+(1—b)(1—b)=0,试求1/ab+ 1/(a+1)(b+1) + 1/(a+2)(b+2)+.+1/(a+2007)(b+2007)的值
|ab-2|+(1-b)(1-b)=0 => |ab-2|=0 ,(1-b)=0
解得b=1,a=2
原式=1/(1*2) + 1/(2*3) + 1/(3*4)+ ...+ 1/(2008*2009)
=(1-1/2) + (1/2-1/3) + (1/3-1/4) +...+(1/2008-1/2009)
=1-1/2009 (中间项消去)
=2008/2009