1/1×2×3+1/2×3×4+1/3×4×5+.+1/48×49×50
来源：学生作业帮助网 编辑：六六作业网 时间：2024/12/24 07:21:28
1/1×2×3+1/2×3×4+1/3×4×5+.+1/48×49×501/1×2×3+1/2×3×4+1/3×4×5+.+1/48×49×501/1×2×3+1/2×3×4+1/3×4×5+.+1/
1/1×2×3+1/2×3×4+1/3×4×5+.+1/48×49×50
1/1×2×3+1/2×3×4+1/3×4×5+.+1/48×49×50
1/1×2×3+1/2×3×4+1/3×4×5+.+1/48×49×50
1/1*3+1/2*4+1/3*5+.+1/48*50=?
1/n(n+2)=[(1/n-1/(n+2)]/2
原式
=[(1/1-1/3)+(1/2-1/4)+……(1/48-1/50)]/2
=(1+1/2-1/49-1/50)/2
=1788/2450
=894/1225