Question

一道初一找规律的数学题,下面是题,我主要要的是讲解啊!

Answer 1

1/ab = 1/(2*1)=1/1-1/2

1/(a+1)(b+1)=1/(3*2)=1/2-1/3

1/(a+2)(b+2)=1/(4*3)=1/3-1/4

……………………

1/(a+2004)(b+2004)=1/2005-1/2006

1/(a+2005)(b+2005)=1/2006-1/2007

以上各式相加得

1-1/2+1/2-1/3+1/3-1/4…………+1/2005-1/2006+1/2006-1/2007

=1-1/2007

=2006/2007