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)
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)