计算:1 (1/1 2) (1/1 2 3) (1/1 2 3 4) …(1/1 2 3 …2009 2010)

=1 (1/3 1/6) (1/10 1/15) (1/21 1/28) … (1/(2009*1004) 1/(2009*2005)) 1/(2011*1005)
=1 1/(1*2) 1/(2*3) 1/(3*4) … 1/(1004*1005) 1/(2011*1005)
=1 1-1/2 1/2-1/3 1/3-1/4 … 1/1004-1/1005 1/(2011*1005)
=1 1-1/1005 1/(2011*1005)
=2-2011/(2011*1005) 1/(2011*1005)
=2-2010/(2011*1005)
=4020/2011

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