(1/1009-1)(1/1010-1).(1/20009-1)(1/2010-1)

分类: 作业答案 • 2022-04-16 23:21:24

问题描述：

(1/1009-1)*(1/1010-1)*.*(1/20009-1)*(1/2010-1)

答

(1/1009-1)*(1/1010-1)*.*(1/2009-1)*(1/2010-1)
=(-1008/1009)*(-1009/1010)*……*(-2008/2009)*(-2009/2010)
=(-1)^1002*1008/2010
=1008/2010

(1/1009-1)*(1/1010-1)*.*(1/20009-1)*(1/2010-1)