1/1X2+1/2X3+1/3X4+...+1/2008X2009

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1/1X2+1/2X3+1/3X4+...+1/2008X20091/1X2+1/2X3+1/3X4+...+1/2008X20091/1X2+1/2X3+1/3X4+...+1/2008X2009通

1/1X2+1/2X3+1/3X4+...+1/2008X2009
1/1X2+1/2X3+1/3X4+...+1/2008X2009

1/1X2+1/2X3+1/3X4+...+1/2008X2009
通式
1/N(N+1)+1/(N+1)(N+2)......=1/1-1/2+1/2-1/3.....+1/2008-1/2009
中间约掉
1-1/2009=2008/2009