这是够简单的了
1 / (2000 X 2001) + 1 / ( 2001 X 2002 ) +……+ 1 / ( 2011 X 2012 ) + 1/2012
= (2001-2000)/(2000X2001) + (2002-2001)/(2001X2002) +……+ (2012-2011)/(2012X2011) + 1/2012
= 1/2000 - 1/2001 + 1/2001 - 1/2002 + 1/2002 +……+ 1/2011 - 1/2012 + 1/2012
= 1/2000