Question

已知|a-1|+(ab-2)²=0求1/(a+1)(b+1)+1/(a+2)(b+2）到1/（a+2008)（b+2008)的

初中一年级

Answer 1

|a-1|+(ab-2)²=0，
a-1=0，ab-2=0，联立解得：a=1,b=2；
1/(a+1)(b+1)+1/(a+2)(b+2）+···+1/（a+2008)（b+2008)
=1/(2×3)+1/(3×4)+···+1/(2009×2010)
用裂项相消法，得
=1/2-1/3+1/3-1/4+···+1/2009-1/2010
=1/2-1/2010
=1004/2010
=502/1005

Answer 2

|a-1|+(ab-2)²=0
因为|a-1|>=0,(ab-2)²>=0
所以a-1=0,ab-2=0
a=1,b=2
1/(a+1)(b+1)+1/(a+2)(b+2)加到1/(a+2008)(b+2008)
=1/(2*3)+1/(3*4)+..+1/(2009*2010)
=1/2-1/3+1/3-1/4+..+-1/2009+1/2009-1/2010
=1/2-1/2010
=502/1005

Answer 3

很明显，a=1 ,b=2

那么，你就带进去算吧