Question

一道数学题，帮帮忙

1 1 1 1
______+______________+______________+............________________
ab (a+1)(b+1) (a+2)(b+2) (a+2008)(b+2008)
其中a=2，b=1

Answer 1

a=2，b=1
所以原式=1/1*2+1/2*3+1/3*4+……+1/2009*2010
=1-1/2+1/2-1/3+1/3-1/4+……+1/2009-1/2010
=1-1/2010
=2009/2010