x-1乘以x-2分之1,+x-2乘以x-3分之1,+x-3乘以x-4分之1,+.+x-99乘以x-100分之

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x-1乘以x-2分之1,+x-2乘以x-3分之1,+x-3乘以x-4分之1,+.+x-99乘以x-100分之
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x-1乘以x-2分之1,+x-2乘以x-3分之1,+x-3乘以x-4分之1,+.+x-99乘以x-100分之
x-1乘以x-2分之1,+x-2乘以x-3分之1,+x-3乘以x-4分之1,+.+x-99乘以x-100分之

x-1乘以x-2分之1,+x-2乘以x-3分之1,+x-3乘以x-4分之1,+.+x-99乘以x-100分之
=[1/(x-2)-1/(x-1)]+[1/(x-3)-1/(x-2)]+……+[1/(x-100)-1/(x-99)]
=-1/(x-1)+1/(x-100)
=99/[(x-1)(x-100)]