1/1x3+1/3x5+1/5x7+.+1/2009x2011
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1/1x3+1/3x5+1/5x7+.+1/2009x20111/1x3+1/3x5+1/5x7+.+1/2009x20111/1x3+1/3x5+1/5x7+.+1/2009x2011原式=1/2×
1/1x3+1/3x5+1/5x7+.+1/2009x2011
1/1x3+1/3x5+1/5x7+.+1/2009x2011
1/1x3+1/3x5+1/5x7+.+1/2009x2011
原式=1/2×(1-1/3)+1/2×(1/3-1/5)+……+1/2×(1/2009-1/2011)
=1/2×(1-1/3+1/3-1/5+……+1/2009-1/2011)
=1/2×(1-1/2011)
=1005/2011