1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+.1/(x-2008)(x-2009)求解

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1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+.1/(x-2008)(x-2009)求解
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1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+.1/(x-2008)(x-2009)求解
1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+.1/(x-2008)(x-2009)求解

1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+.1/(x-2008)(x-2009)求解
=-[1/(x-1)-1/(x-2)+1/(x-2)-1/(x-3)+1/(x-3)-……-1/(x-2008)+1/(x-2008)-1/(x-2009)]
=-[1/(x-1)-1/(x-2009)]
=-[(x-2009)-(x-1)]/(x-1)(x-2009)
=2008/(x-1)(x-2009)
看其中的一个1/(x-1)(x-2)
=-[(x-2)-(x-1)]/(x-1)(x-2)=-[(x-2)/(x-1)(x-2)-(x-1)/(x-1)(x-2)]=-[1/(x-1)-1/(x-2)]
其它一样