1/1*3+1/3*5+1/5*7+.+1/2007*2009+1/2009*2011

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1/1*3+1/3*5+1/5*7+.+1/2007*2009+1/2009*20111/1*3+1/3*5+1/5*7+.+1/2007*2009+1/2009*20111/1*3+1/3*5+1/

1/1*3+1/3*5+1/5*7+.+1/2007*2009+1/2009*2011
1/1*3+1/3*5+1/5*7+.+1/2007*2009+1/2009*2011

1/1*3+1/3*5+1/5*7+.+1/2007*2009+1/2009*2011
原式=1/2(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9……+1/2007-1/2009+1/2009-1/2011)
=1/2(1-1/2011)=1005/2011

1/1*3+1/3*5+1/5*7+........+1/2007*2009+1/2009*2011
=(1-1/3+1/3-1/5.....-1/2011)*3
=1/2010*3
=1/670