1/1*2+1/2*3+1/3*4+1/4*5+.+1/2005*2006
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/03 04:35:17
![1/1*2+1/2*3+1/3*4+1/4*5+.+1/2005*2006](/uploads/image/z/13826602-10-2.jpg?t=1%2F1%2A2%2B1%2F2%2A3%2B1%2F3%2A4%2B1%2F4%2A5%2B.%2B1%2F2005%2A2006)
1/1*2+1/2*3+1/3*4+1/4*5+.+1/2005*2006
1/1*2+1/2*3+1/3*4+1/4*5+.+1/2005*2006
1/1*2+1/2*3+1/3*4+1/4*5+.+1/2005*2006
1/1*2+1/2*3+1/3*4+1/4*5+.+1/2005*2006
=1-1/2+1/2-1/3+1/3-1/4+.+1/2005-1/2006
=1-1/2006
=2005/2006
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/2005-1/2006)
=1-1/2006
=2005/2006
两个连续自然数倒数的积等于倒数的差