Question

如果有理数a，b满足|ab-2|+|1-b|=0.

如果有理数a，b满足|ab-2|+|1-b|=0.试求1/ab+1/(a+1)(b+1)+1(a+2)(b+2)+…+1/(a+2008)(b+2008)的值
回答的话请你们写清楚一点,因为我似乎不是很聪明的样子,谢谢了

Answer 1

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

Answer 2

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

Answer 3

=2009/2010