1/12+1/23+1/34+1/45.+1/20072008+1/20082009=?

来源：学生作业帮助网编辑：作业帮时间：2024/04/29 00:45:58

1/1*2+1/2*3+1/3*4+1/4*5.+1/2007*2008+1/2008*2009=?
1/1*2+1/2*3+1/3*4+1/4*5.+1/2007*2008+1/2008*2009=?

1/1*2+1/2*3+1/3*4+1/4*5.+1/2007*2008+1/2008*2009=?
原式=(1-1/2)+(1/2-1/3)+(1/3-1/4)+…+(1/2007-1/2008)+(1/2008-1/2009)=1-1/2009=2008/2009.

1/1*2 1/2*3 1/3*4 1/4*5 ......... 1/2007*2008 1/2008*2009
=1-1/2 1/2-1/3 1/3-1/4 1/4-1/5 ... 1/2008-1/2009
=1-1/2009
=2008/2009