化简1/(X(X-1))+1/((X-1)(X-2))+1/((X-2)(X-3))+……+1/((X-2009)(X-2010))过程

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化简1/(X(X-1))+1/((X-1)(X-2))+1/((X-2)(X-3))+……+1/((X-2009)(X-2010))过程
化简1/(X(X-1))+1/((X-1)(X-2))+1/((X-2)(X-3))+……+1/((X-2009)(X-2010))
过程

化简1/(X(X-1))+1/((X-1)(X-2))+1/((X-2)(X-3))+……+1/((X-2009)(X-2010))过程
1/(X(X-1))=1/x-1/(x-1)
1/((X-1)(X-2))=1/(x-1)-1/(x-2)
……
1/((X-2009)(X-2010))=1/(x-2009)-1/(x-2010)
所以1/(X(X-1))+1/((X-1)(X-2))+1/((X-2)(X-3))+……+1/((X-2009)(X-2010))=
[1/x-1/(x-1)]+[1/(x-1)-1/(x-2)]+……+[1/(x-2009)-1/(x-2010)]=
1/x-1/(x-2010)