a=1 b=2求 1/ab+ 1/(a+1)+(b+1)+ 1/(a+2)(b+2)……………………1/(a+2008)(a+2009)是1/(a+2008)(b+2008)

a=1 b=2
求 1/ab+ 1/(a+1)+(b+1)+ 1/(a+2)(b+2)……………………1/(a+2008)(a+2009)
是1/(a+2008)(b+2008)

题目有些乱,最后一项不对吧,是不是1/(a+2008)(b+2008)?
根据题意,
原式=1/(1*2)+1/(2*3)+1/(3*4)+...+1/(2009*2010)
1/(1*2)=1-1/2
1/(2*3)=1/2-1/3
.
1/(2009*2010)=1/2009-1/2010
所以,
原式
=1-1/2+1/2-1/3+...+1/2009-1/2010
=1-1/2010
=2009/2010
如果题目不对,检查后再hi我吧