1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)……1/(a+2005)(b+2005)=?

分类: 作业答案 • 2022-05-24 19:50:20

问题描述：

1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)……1/(a+2005)(b+2005)=?
a=2,b=1

答

=1/(2*1)+1/(3*2)+1/(4*3)……1/(2007*2006)
=1-1/2+1/2-1/3+1/3-1/4……1/2006-1/2007
=1-1/2007
=2006/2007