计算:1/1×3+1/3×5+1/5×7+……+1/2005×2007+1/2007×2009
问题描述：
计算:1/1×3+1/3×5+1/5×7+……+1/2005×2007+1/2007×2009
答
裂项
1/1×3=(1/1-1/3)/2;
……
类推
得结果为（1-1/2009)/2=
答
原式=(1/2)*(1/1-1/3+1/3-1/5+1/5-1/7+...+1/2005-1/2007+1/2007-1/2009)
=(1/2)*(1/1-1/2009)=1004/2009