03*5/1+5*7/1+7*9/1...+2007*2009/1

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03*5/1+5*7/1+7*9/1...+2007*2009/1
03*5/1+5*7/1+7*9/1...+2007*2009/1

03*5/1+5*7/1+7*9/1...+2007*2009/1
3*5/1+5*7/1+7*9/1...+2007*2009/1
=1/2* (1/3-1/5+1/5-1/7+.+1/2007-1/2009)
=1/2*(1/3-1/2009)
=1003/6027

1/(3×5)+1/(5×7)+1/(7×9)+……+1/(2007×2009)
=2(1/3-1/5)+2(1/5-1/7)+2(1/7-1/9)+……+2(1/2007-1/2009)
=2(1/3-1/5+1/5-1/7+1/7-1/9+……+1/2007-1/2009)
=2(1/3-1/2009)
=4012/6027