计算1/1×3+1/3×5+1/5×7+…+1/1997×1999

问题描述:

计算1/1×3+1/3×5+1/5×7+…+1/1997×1999

1/1×3+1/3×5+1/5×7+…+1/1997×1999
=1/2[1/1-1/3+1/3-1/5+1/5-1/7+...+1/1997-1/1999]
=1/2[1-1/1999]
=999/1999