如果有理数a,b满足|ab-2|+(1-b)^2=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)…+1/(a+_数学解答

如果有理数a,b满足|ab-2|+(1-b)^2=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)…+1/(a+2007）(b+2007)的值：

人气：407 ℃　时间：2020-03-26 21:21:30

解答

由已知得b=1 a=2
所以式子等于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)=2008/2009