作业帮1/1*2+1/2*3+1/3*4+.+1/998*999+1/999*1000
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/20 10:40:08
x)372672Z&z@B̲2400I*'^~
) **,c02 kkӄ,<`Xrgk2Yg: BUAx@]~qAb _6`γM v=|l/7\橸 x=Ǜ |
]˞u=m Pw@E ,a3P㴡hCjCj#yE#`C `,~ e{ơ
1/1*2+1/2*3+1/3*4+.+1/998*999+1/999*1000
1/1*2+1/2*3+1/3*4+.+1/998*999+1/999*1000
1/1*2+1/2*3+1/3*4+.+1/998*999+1/999*1000
1/1*2+1/2*3+1/3*4+.+1/998*999+1/999*1000
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/998-1/999)+(1/999-1/1000)
中间正负抵消
=1-1/1000
=999/1000
没分不答
裂项法
1/1*2+1/2*3+1/3*4+...........+1/998*999+1/999*1000
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+....+(1/998-1/999)+(1/999-1/1000)中间约掉
=1-1/1000
=999/1000
1/1*2=1/1-1/2
1/2*3=1/2-1/3
1/3*4=1/3-1/4
……
……
原式＝1/1-1/2+1/2-1/3+1/3-1/4+……+1/998-1/999+1/999-1/1000
=1-1/1000
=999/1000