1/1*3+1/3*5+1/5*7+...+1/2010*2011
=1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+.+1/2(1/2009-1/2011)
=1/2(1-1/3+1/3-1/5+1/5-1/7+.+1/2009-1/2011)
=1/2(1-1/2011)
=1/2*2010/2011
=1005/2011