1/6+1/12+1/20+1/30+...=1/2005*2006
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/02 00:42:01
![1/6+1/12+1/20+1/30+...=1/2005*2006](/uploads/image/z/265201-25-1.jpg?t=1%2F6%2B1%2F12%2B1%2F20%2B1%2F30%2B...%3D1%2F2005%2A2006)
1/6+1/12+1/20+1/30+...=1/2005*2006
1/6+1/12+1/20+1/30+...=1/2005*2006
1/6+1/12+1/20+1/30+...=1/2005*2006
原式
=1/2x3+1/3x4+1/4x5+……+1/2005x2006
=1/2-1/3+1/3-1/4+1/4-1/5+……+1/2005-1/2006
=1/2-1/2006
=1003/2006-1/2006
=1002/2006
=501/1003
1/6+1/12+1/20+1/30+.......+1/2005*2006=
=[1/(2*3)]+[1/(3*4)]+[1/(4*5)]+[1/(5*6)]+……+[1/(2005*2006)]
=(1/2)-(1/3)+(1/3)-(1/4)+(1/4)-(1/5)+(1/5)-(1/6)+……+(1/2005)-(1/2006)
=(1/2)-(1/2006)
=1002/2006
=501/1003
以上回答你满意么?