1/(x-1)+1/(x-1)(x-2)+...+1/(x-2010)(x-2011)
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1/(x-1)+1/(x-1)(x-2)+...+1/(x-2010)(x-2011)1/(x-1)+1/(x-1)(x-2)+...+1/(x-2010)(x-2011)1/(x-1)+1/(x-1
1/(x-1)+1/(x-1)(x-2)+...+1/(x-2010)(x-2011)
1/(x-1)+1/(x-1)(x-2)+...+1/(x-2010)(x-2011)
1/(x-1)+1/(x-1)(x-2)+...+1/(x-2010)(x-2011)
利用：1/(x-(n+1))- 1/(x-n)=1/(x-n)(x-(n+1)) 来解
如：1/(x-2)- 1/(x-1)=1/(x-1)(x-2)
所以：1/(x-1)+1/(x-1)(x-2)+...+1/(x-2010)(x-2011)
=1/(x-1)+ 1/(x-2)- 1/(x-1)+……+1/(x-2011)- 1/(x-2010)
=1/(x-2011)
原题变形为：1/（x-1）+1/(x-2)-1/(x+1)+...+1/(x-2011)-1/(x-2010)=1/(x-2011)
1/(x-2011)
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