1/1×1/2×1/3+1/2×1/3×1/4+1/3×1/4×1/5+...+1/48×1/49×1/50
来源：学生作业帮助网 编辑：六六作业网 时间：2024/12/20 04:11:09
1/1×1/2×1/3+1/2×1/3×1/4+1/3×1/4×1/5+...+1/48×1/49×1/501/1×1/2×1/3+1/2×1/3×1/4+1/3×1/4×1/5+...+1/48×1
1/1×1/2×1/3+1/2×1/3×1/4+1/3×1/4×1/5+...+1/48×1/49×1/50
1/1×1/2×1/3+1/2×1/3×1/4+1/3×1/4×1/5+...+1/48×1/49×1/50
1/1×1/2×1/3+1/2×1/3×1/4+1/3×1/4×1/5+...+1/48×1/49×1/50
=1/1×2×3+1/2×3×4+……+1/48×49×50
=1/2×(1/1×2-1/2×3+1/2×3-1/3×4+……+1/48×49-1/49×50)
=1/2×(1/1×2-1/49×50)
=306/1225