计算:2/3+2/15+2/35+2/63+......+2/9603=?

问题描述:

计算:2/3+2/15+2/35+2/63+......+2/9603=?

2/3+2/15+2/35+2/63+……+2/9603=2/3+2/(3×5)+2/(5×7)+2/(7×9)+……2/(97×99)=2/3+1/2×(1/3-1/5)+1/2×(1/5-1/7)+1/2×(1/7-1/9)+……1/2×(1/97-1/99)=2/3+1/2×(1/3-1/5+1/5-1/7+1/7-1/9+…...