(1×3)分之1+(3×5)分之1+(5×7)分之1+...+(2011×2013)分之1,

题目

(1×3)分之1+(3×5)分之1+(5×7)分之1+...+(2011×2013)分之1,

答案

1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+...+1/2(1/2011-1/2013)
=1/2(1-1/3+1/3-1/5+1/5-1/7+...+1/2011-1/2013)
=1/2(1-1/2013)
=1006/2013