1/1X2+1/2X3+1/3X4+1/4X5+...+1/2010X2011

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1/1X2+1/2X3+1/3X4+1/4X5+...+1/2010X20111/1X2+1/2X3+1/3X4+1/4X5+...+1/2010X20111/1X2+1/2X3+1/3X4+1/4X

1/1X2+1/2X3+1/3X4+1/4X5+...+1/2010X2011
1/1X2+1/2X3+1/3X4+1/4X5+...+1/2010X2011

1/1X2+1/2X3+1/3X4+1/4X5+...+1/2010X2011
做了将近半个小时没做出来,突然想出来了,该题好像在课本上有,觉得太简单了.
将题目化为:1/nx(n+1)=1/n---1/(n+1)带入式子得:中间的全消掉了,
最后剩下的是1-1/2011=2010/2011!