智慧题1/(x-1)(x-2)+1/(x-2)(x-3)+.+1/(x-2004)(x-2005)等

网友回答

1/(x-1)(x-2)+1/(x-2)(x-3)+.+1/(x-2004)(x-2005)
=1/(x-2)-1/(x-1)+1/(x-3)-1/(x-2)+.+1/(x-2005)-1/(x-2004)
=1/(x-2005)-1/(x-1)
=2004/[(x-2005)(x-1)]
======以下答案可供参考======
供参考答案1:
原式=1/(x-2005)-1/(x-2004)+1/(x-2004)-1/(x-2003)+……+1/(x-2)-1/(x-1)
=1/(x-2005)-1/(x-1)
=2004/[(x-2005)*(x-1)]
供参考答案2:
将分母拆开有1/（X-1)(X-2)=1/(X-1）—1/（X-2）
所以最后是 -2004/（X-1）（X-2005）