1/1x2+1/2x3+1/3x4+1/4x5+……1/8x9+1/9x10=?(简便算法)快~~~~~

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1/1x2+1/2x3+1/3x4+1/4x5+……1/8x9+1/9x10=?(简便算法)快~~~~~

1/1x2+1/2x3+1/3x4+1/4x5+……1/8x9+1/9x10=?(简便算法)快~~~~~
1/1x2+1/2x3+1/3x4+1/4x5+……1/8x9+1/9x10=?(简便算法)
快~~~~~

1/1x2+1/2x3+1/3x4+1/4x5+……1/8x9+1/9x10=?(简便算法)快~~~~~
1/1x2+1/2x3+1/3x4+1/4x5+……1/8x9+1/9x10
=1-1/2+1/2-1/3+1/3-1/4+.+1/8-1/9+1/9-1/10
=1-1/10
=9/10

1/1x2=1/1-1/2
1/2x3=1/2-1/3
...
1/9x10=1/9-1/10
1/1x2+1/2x3+1/3x4+1/4x5+……1/8x9+1/9x10=1-1/10=9/10

1/1x2+1/2x3+1/3x4+1/4x5+……1/8x9+1/9x10
=1-1/2+1/2-1/3+1/3-1/4+……+1/9-1/10
中间全部抵消
=1-1/10
=9/10
公式:1/m*n=1/m-1/n
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裂项相消。
公式应是1/m*n=(1/m-1/n)*(n-m)