已知|ab-2|+|a-1|=0.求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2013)(b+2013)的值
问题描述:
已知|ab-2|+|a-1|=0.求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2013)(b+2013)的值
答
依题意
a-1=0
ab-2=0
由此得到
a=1,b=2
代入
1/2+1/(2*3)+1/(3*4)+.+1/(2007*2008)+1/(2014*2015)
=1-1/2+1/2-1/3+1/3-1/4+.+1/2007-1/2008+1/2014-1/2015
=1-1/2015
=2014/2015