1/1x3+1/3x5+1/5x7+.+1/2009x2011=
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1/1x3+1/3x5+1/5x7+.+1/2009x2011=1/1x3+1/3x5+1/5x7+.+1/2009x2011=1/1x3+1/3x5+1/5x7+.+1/2009x2011=1/1x
1/1x3+1/3x5+1/5x7+.+1/2009x2011=
1/1x3+1/3x5+1/5x7+.+1/2009x2011=
1/1x3+1/3x5+1/5x7+.+1/2009x2011=
1/1x3+1/3x5+1/5x7+.+1/2009x2011
=(1/2)*(1-1/3+1/3-1/5+1/5-1/7_.+1/2009-1/2011)
=(1/2)*(1-1/2011)
=1005/2011
1005/2011