UC知道请问1/1*2+1/2*3+1/3*4+1/4*5+.........1/2006*2007=?
来源：百度知道 编辑：UC知道 时间：2024/07/04 15:57:53
其中/表示分号，*表示乘号
1/1*2+1/2*3+1/3*4+1/4*5+.........1/2006*2007
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5).........+ (1/2006-1/2007)(变形)
=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5.........+ 1/2006- 1/2007 (去括号)
=1/1-1/2007
=2006/2007
1/1*2=1-1/2
1/2*3=1/2-1/3
......
1/2006*2007=1/2006-1/2007
所以原式=1-1/2+1/2-1/3+1/3-1/4+....+1/2006-1/2007
=1-1/2007
=2006/2007
1/1*2+1/2*3+1/3*4+1/4*5+.........1/2006*2007
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5).........+ (1/2006-1/2007)
=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5.........+ 1/2006- 1/2007
=1/1-1/2007
=2006/2007
2006/2007
2006/2007
2006/2007