解:1/1×3+1/3×5+1/5×7+.+1/2013×2015=1/2×(1-1/3)+1/2×(1/3-1/5)+…+1/2×(1/2013-1/2015)=1/2×(1-1/3+1/3-1/5+.+1/2013-1/2015)=1/2×（1-1/2015）=1/2×2014/2015=1007/2015
