1/1X2 +1/2X3+1/3X4+……1/10X11

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/25 01:27:52
1/1X2+1/2X3+1/3X4+……1/10X111/1X2+1/2X3+1/3X4+……1/10X111/1X2+1/2X3+1/3X4+……1/10X111/1X2+1/2X3+1/3X4+…

1/1X2 +1/2X3+1/3X4+……1/10X11
1/1X2 +1/2X3+1/3X4+……1/10X11

1/1X2 +1/2X3+1/3X4+……1/10X11
1/1X2 +1/2X3+1/3X4+……1/10X11
=(1/1-1/2)+(1/2-1/3)+……+(1/10-1/11)
=1/1-1/11
=10/11

1/n×(n+1)=1/n-1/(n+1)
1/1×2+1/2×3+...+1/10×11
=(1/1-1/2)+(1/2-1/3)+...+(1/10-1/11)
=1-1/11
=10/11

=(1-1/2)+(1/2-1/3)+......(1/10-1/11)=1-1/11=10/11

解:利用公式1/n*(n+1)=(1/n)-(1/n+1).
原式=1-1/2+1/2-1/3......+1/10-1/11
=1-1/11
=10/11

如果想证明公式,倒过来算算就行了.