如果有理数a,b满足|ab-2|+(1-b)^2=0试求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
试求1／ab+1/(a+1 )(b+1)+1/(a+2)(b+2)+…1/（a+2009)（b+2009）的值

人气：418 ℃　时间：2020-04-08 18:02:42

解答

|ab-2|=0(1-b)^2=0 所以b=1,a=21／ab+1/(a+1 )(b+1)+1/(a+2)(b+2)+…1/（a+2009)（b+2009）=1/2+1/(3*2)+1/(4*3)+...+1/(2011*2010)=1/2+(1/2-1/3)+(1/3-1/4)+...+(1/2010-1/2011)=1-1/2011=2010/2011