如果|ab--2|+(b-1)平方=o,试求1/ab+1/(a+1)(b+1)+…+1/(a+2008)(b+2008)的值

题目

如果|ab--2|+(b-1)平方=o,试求1/ab+1/(a+1)(b+1)+…+1/(a+2008)(b+2008)的值

答案

ab-2=0,ab=2; b-1=0,b=1,a=2
1/ab+1/(a+1)(b+1)+…+1/(a+2008)(b+2008)
=1/2+1/3*2+…+1/2010*2009
=1-1/2+1/2-1/3+…+1/2009-1/2010
=1-1/2010
=2009/2010