Question

如果有理数啊，a,b满足|ab-2|+(1-b)的二次方=0，试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+

1/(a+2008)(b+2008)的值

Answer 1

由|ab-2|+(1-b)的二次方=0 可以得知 ab=2，1-b=0 所以 a=2，b=1
然后你带入就知道了 最后结果是2009/2010. 望采纳

Answer 2

|ab-2|+(1-b)²=0
ab-2=0
1-b=0
b=1,a=2
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2008)(b+2008)
=1/2+1/6+1/12+......+1/(2009×2008)
=1-1/2+1/2-1/3+1/3-1/4+......+1/2008-1/2009
=1-1/2009
=2008/2009

Answer 3

ab-2=0
1-b=0
b=1,a=2
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2008)(b+2008)
=1/2+1/(2*3)+1/(3*4)1+......+1/(2009×2010)
=1-1/2+1/2-1/3+1/3-1/4+......+1/2009-1/2010
=1-1/2010
=2009/2010