已知a=1,b=2.求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2008)(b+2008)

分类: 作业答案 • 2022-07-07 10:24:54

问题描述：

答

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