1×3分之1+3×5分之1+5×7分之1.+2009×2011分之1 +2011×2013分之1等于?
问题描述：
1×3分之1+3×5分之1+5×7分之1.+2009×2011分之1 +2011×2013分之1等于?
答
1/(1×3)+1/(3×5)+1/(5×7)+...+1/(2011×2013)
=1/2(1/1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+...+1/2(1/2011-1/2013)
=1/2×1-1/2×1/3+1/2×1/3-1/2×1/5+1/2×1/5-1/2×1/7+...+1/2×1/2011-1/2×1/2013
=1/2-1/2×1/2013
=1/2×(1-1/2013)
=1/2×2012/2013
=1006/2013