/表示分数线时,习惯分子写在前面,分母写在后面
1/1×3+1/3×5+1/5×7+...+1/2001×2003
=(1/2)×[2/1×3+2/3×5+2/5×7+...+2/2001×2003]
=(1/2)×[(1/1-1/3)+(1/3-1/5)+(1/5-1/7)+...+(1/2001-1/2003)]
=(1/2)×(1-1/3+1/3-1/5+1/5-1/7+...+1/2001-1/2003)
=(1/2)×(1-1/2003)
=(1/2)×(2009/2011)
=1001/2011