作业帮1/1×2×3+1/2×3×4+1/3×4×5+1/4×5×6+.+1/48×49×50怎么算
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/16 00:31:20
1/1×2×3+1/2×3×4+1/3×4×5+1/4×5×6+.+1/48×49×50怎么算
1/1×2×3+1/2×3×4+1/3×4×5+1/4×5×6+.+1/48×49×50怎么算
1/1×2×3+1/2×3×4+1/3×4×5+1/4×5×6+.+1/48×49×50怎么算
等于1/4啊 !
裂项求和
如1/1*2*3=1/2(1/1*2-1/2*3)
1/2*3*4=1/2(1/2*3-1/3*4)以此类推
最后等于1/4
答案是612/25,因为1/n(n+1)(n+2)=1/(2n)-1/(n+1)+1/(2(n+2)), 剩下的自己琢磨
1/1×2×3+1/2×3×4+1/3×4×5+......+1/48×49×50
原式= 1/2[(1/1×2-1/2×3) +(1/2×3-1/3×4) +(1/3×4-1/4×5) +......+(1/48×49-1/49×50)]
= 1/2[1/2-1/49×50]
= 1/4-1/4900
= 306/1225
简雪峰仅作参考